A Comparison of Various Definitions of Contractive Mappings

From MaRDI portal

Publication:4141794

Jump to:navigation, search

DOI10.2307/1997954zbMath0365.54023OpenAlexW4240914667MaRDI QIDQ4141794

Billy E. Rhoades

Publication date: 1977

Full work available at URL: https://doi.org/10.2307/1997954

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25)

Related Items

Volterra integral equations on variable exponent Lebesgue spaces ⋮ On fixed points of locally and pointwise contracting maps ⋮ Unified relation-theoretic metrical fixed point theorems under an implicit contractive condition with an application ⋮ Fixed point results in \(C^{*}\)-algebra-valued metric spaces are direct consequences of their standard metric counterparts ⋮ Coincidence point theorems for generalized contractions with application to integral equations ⋮ Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators ⋮ On an extension of contractivity conditions via auxiliary functions ⋮ An extension of the contraction mapping principle to Lipschitzian mappings ⋮ Stability and convergence of a new composite implicit iterative sequence in Banach spaces ⋮ Some results in fixed point theory and application to the convergence of some iterative processes ⋮ A remark on discontinuity at fixed point ⋮ Common fixed points for generalized contractive multivalued operators in complete metric spaces ⋮ A hybrid class of expansive-contractive mappings in cone \(b\)-metric spaces ⋮ \({\psi F}\)-contractions: not necessarily nonexpansive Picard operators ⋮ Coincidence and common fixed points of Perov type generalized Ćirić-contraction mappings ⋮ Employing common limit range property to prove unified metrical common fixed point theorems ⋮ Some fixed point theorems for Prešić-Hardy-Rogers type contractions in metric spaces ⋮ Functional contractive maps in triangular symmetric spaces ⋮ Fixed points of multivalued nonself almost contractions ⋮ Round-off stability for multi-valued maps ⋮ Coincidence points of mappings and relations with applications ⋮ A rate of convergence for asymptotic contractions ⋮ Common fixed point theorems for nonlinear contractive mappings in dislocated metric spaces ⋮ Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces ⋮ Common fixed points of mappings satisfying implicit contractive conditions ⋮ Common fixed points of \(g\)-quasicontractions and related mappings in 0-complete partial metric spaces ⋮ Fixed point results under various contractive conditions in partial metric spaces ⋮ On iterations for families of asymptotically pseudocontractive mappings ⋮ Fixed point theorems for \((\xi,\alpha)\)-expansive mappings in complete metric spaces ⋮ Fixed point theorems under Hardy-Rogers contractive conditions on 0-complete ordered partial metric spaces ⋮ Cone metric spaces and fixed point theorems of contractive mappings ⋮ The contraction principle for set valued mappings on a metric space with a graph ⋮ A new approach to fixed point theorems on \(G\)-metric spaces ⋮ Fixed and periodic point theory in certain spaces ⋮ Coupled fixed-point results for \(T\)-contractions on cone metric spaces with applications ⋮ Three extensions of Ćirić quasicontraction on partial metric spaces ⋮ New generalized pseudodistance and coincidence point theorem in a \(b\)-metric space ⋮ Fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces ⋮ A fixed point theorem for generalized \(F\)-contractions on complete metric spaces ⋮ Coupled fixed point theorems for contractions in intuitionistic fuzzy normed spaces ⋮ A generalization of Ćirić quasicontractions ⋮ Comparison of the rate of convergence among Picard, Mann, Ishikawa, and Noor iterations applied to quasicontractive maps ⋮ On a Suzuki type general fixed point theorem with applications ⋮ Some fixed point theorem for expansive type mapping in dislocated metric space ⋮ On mappings with contractive iterate at a point in generalized metric spaces ⋮ Common fixed point results in metric-type spaces ⋮ Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces ⋮ Some results on the continuous dependence of the fixed points for Kirk-type iterative processes in Banach space ⋮ A fixed point theorem for weakly Zamfirescu mappings ⋮ Common fixed points of generalized contractions on partial metric spaces and an application ⋮ Fixed point theorems for generalized weakly contractive mappings ⋮ Fixed point theorems by ways of ultra-asymptotic centers ⋮ Nonlinear contractions in \(0\)-complete partial metric spaces ⋮ An integral type fixed point theorem for multi-valued mappings employing strongly tangential property ⋮ On generalizations of the Meir-Keeler type contraction maps ⋮ New fixed point theorems for asymptotically regular multi-valued maps ⋮ Random fixed point theorems for commuting random operators in probabilistic functional analysis ⋮ Jungck's common fixed point theorem and E.A property ⋮ Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space ⋮ \(T\)-stability of Picard iteration in metric spaces ⋮ Data dependence for Ishikawa iteration when dealing with contractive-like operators ⋮ Fixed point theorems on generalized metric spaces for mappings in a class of almost \(\varphi\)-contractions ⋮ Presic type fixed point theorem for four maps in metric spaces ⋮ Some relations between \(n\)-tuple fixed point and fixed point results ⋮ Some coincidence theorems and stability of iterative procedures ⋮ Some extensions of Banach's contraction principle in complete cone metric spaces ⋮ Synthetic approaches to problems of fixed points in metric space ⋮ A generalization of Hegedüs-Szilágyi's fixed point theorem in complete metric spaces ⋮ Some results on multi-valued weakly Jungck mappings in \(b\)-metric space ⋮ Boyd-Wong-type common fixed point results in cone metric spaces ⋮ Coincidence theorems for certain classes of hybrid contractions ⋮ Fixed points of multivalued operators in ordered metric spaces with applications ⋮ The fixed point theory for some generalized nonexpansive mappings ⋮ Common fixed point theorems for a finite family of discontinuous and noncommutative maps ⋮ Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces ⋮ Approximation of common fixed points of weakly compatible pairs using the Jungck iteration ⋮ Generalized \(\varphi \)-contraction for a pair of mappings on cone metric spaces ⋮ A best proximity point theorem for weakly contractive non-self-mappings ⋮ Fractals via iterated functions and multifunctions ⋮ On Naimpally and Singh's open questions ⋮ Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces ⋮ Common fixed points for \((g, f)\) type maps in cone metric spaces ⋮ Extensions of some fixed point theorems of Rhoades ⋮ Fixed-point theorems for families of weakly non-expansive maps ⋮ Common fixed points for multivalued generalized contractions on partial metric spaces ⋮ Generalized nonexpansive mappings in ordered metric spaces and their (common) fixed points with applications ⋮ Coincidence and fixed point for weakly reciprocally continuous single-valued and multi-valued maps ⋮ Common tripled fixed point results in cone metric type spaces ⋮ Random coincidence points of expansive type completely random operators ⋮ Fixed points for contractive mappings of third order in pseudo- quasimetric spaces ⋮ Fixed points of multivalued maps in modular function spaces ⋮ Common fixed point theorems for weakly compatible pairs on cone metric spaces ⋮ Common fixed points of two maps in cone metric spaces ⋮ Strict contractive conditions and common fixed point theorems in cone metric spaces ⋮ Assad-Kirk-type fixed point theorems for a pair of nonself mappings on cone metric spaces ⋮ A continuation method for weakly contractive mappings under the interior condition ⋮ On some common fixed point theorems with rational expressions over closed subset of a Hilbert space ⋮ Cyclic iterated function systems ⋮ The convergence theorems of the sequence of Ishikawa iterates for hemicontractive mappings ⋮ \(\alpha\)-\(\psi\)-Geraghty contractions on generalized metric spaces ⋮ Coincidence point theorems on quasi-metric spaces via simulation functions and applications to \(G\)-metric spaces ⋮ Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps ⋮ Fractal functions on the Sierpinski gasket ⋮ Interpolative Caristi type contractive mapping in an extended \(b\)-metric space ⋮ Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph ⋮ Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions ⋮ Multi-valued versions of Nadler, Banach, Branciari and Reich fixed point theorems in double controlled metric type spaces with applications ⋮ Some fixed point results on generalized metric spaces ⋮ Generalized fractals in semimetric spaces ⋮ Relation theoretic metrical fixed point results for Suzuki type \(\mathcal{Z}_{\mathcal{R}}\)-contraction with an application ⋮ Common fixed point theorems for some new generalized contractive type mappings ⋮ Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications ⋮ New fixed point results for Proinov-Suzuki type contractions in metric spaces ⋮ Berinde mappings in orbitally complete metric spaces ⋮ On generalized Pata type contractions ⋮ Some new fixed point theorems in partial metric spaces with applications ⋮ Triple fixed point theorems via \(\alpha\)-series in partially ordered metric spaces ⋮ On the sum of contractive type of mappings II: Maps on different classes ⋮ A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces ⋮ Some new fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces ⋮ Fixed points of mappings satisfying contractive condition of integral type in modular spaces endowed with a graph ⋮ Some new contractive mappings on \(S\)-metric spaces and their relationships with the mapping (S25) ⋮ Fixed points of convex and generalized convex contractions ⋮ Fixed point theorems for generalized semi-quasi contractions ⋮ A unique common triple fixed point theorem for hybrid pair of maps ⋮ Some fixed and periodic points in abstract metric spaces ⋮ Some generalizations of Jungck's fixed point theorem ⋮ Generalisations, examples, and counter-examples in analysis and optimisation. \textit{In honour of Michel Théra at 70} ⋮ A generalization of Nadler's fixed point theorem ⋮ Extensions of the Zamfirescu theorem to partial metric spaces ⋮ On iterated function systems consisting of Kannan maps, Reich maps, Chatterjea type maps, and related results ⋮ Fixed and best proximity points for Kannan cyclic contractions in modular function spaces ⋮ On regular semimetric spaces having strong triangle functions ⋮ Particle-SfT: a provably-convergent, fast shape-from-template algorithm ⋮ An observation on \(F\)-weak contractions and discontinuity at the fixed point with an application ⋮ Nonlinear fractal interpolation curves with function vertical scaling factors ⋮ Remarks on generalized contractions ⋮ Coincidence and fixed point theorems for generalized \((\psi,\phi)\)-weak nonlinear contraction in ordered \(K\)-metric spaces ⋮ On multivalued hybrid contractions with applications ⋮ A minimal continuity condition and existence of common fixed points ⋮ Coupled fixed-point theorems for contractions in partially ordered metric spaces and applications ⋮ New types of fractal interpolation surfaces ⋮ Topological vector space-valued cone metric spaces and fixed point theorems ⋮ Remarks on recent fixed point theorems ⋮ Data dependence results of new multi-step and S-iterative schemes for contractive-like operators ⋮ Some convergence results for iterative sequences of Prešić type and applications ⋮ The extension of fixed point theorems for set valued mapping ⋮ On modified \((\alpha - \eta)\)-contractive mappings ⋮ Kannan's fixed point approximation for solving split feasibility and variational inequality problems ⋮ Cyclic (\(\phi\))-contractions in uniform spaces and related fixed point results ⋮ Homotopic metric-interval L-contractions in gauge spaces ⋮ Analytic methods in Rhoades contractions theory ⋮ Fixed point property of a nonempty set relative to the class of friendly mappings ⋮ A new idea to construct the fractal interpolation function ⋮ Best proximity point results for Hardy-Rogers \(p\)-proximal cyclic contraction in uniform spaces ⋮ A common fixed point theorem for nonlinear quasi-contractions on \(b\)-metric spaces with application in integral equations ⋮ Two generalized common fixed point theorems involving compatibility and property E.A. ⋮ A new extension of Kannan contractions and related fixed point results ⋮ On the strong and \(\delta\)-convergence of new multi-step and \(S\)-iteration processes in a \(\mathrm{CAT}(0)\) space ⋮ On convergence results for Lipschitz pseudocontractive mappings ⋮ Fixed point theorem on two complete cone metric spaces ⋮ Approximating best proximity points for Reich type non-self nonexpansive mappings ⋮ Iterative fixed point theorems in \(E\)-metric spaces ⋮ Coincidence and fixed points for hybrid strict contractions ⋮ Fixed point theorems for generalized \(F\)-Suzuki-contraction mappings in complete \(b\)-metric spaces ⋮ On multiplicative metric spaces: survey ⋮ Data dependence results for multistep and CR iterative schemes in the class of contractive-like operators ⋮ Efficacy of coefficients on rate of convergence of some iteration methods for quasi-contractions ⋮ Fixed point theorems for asymptotically regular semigroups equipped with generalized Lipschitzian conditions in metric spaces ⋮ Some new observations on generalized contractive mappings and related results in \(b\)-metric-like spaces ⋮ Locally weak version of the contraction mapping principle ⋮ A countable fractal interpolation scheme involving Rakotch contractions ⋮ Fixed points of Kannan contractive mappings in relational metric spaces ⋮ Simulation functions and Boyd-Wong type results ⋮ Some fixed point results in partial rectangular metric-like spaces ⋮ Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative algorithm in Banach spaces ⋮ \((\psi, \phi)\)-Wardowski contraction pairs and some applications ⋮ On surrounding quasi-contractions on non-triangular metric spaces ⋮ A survey of fixed point theorems under Pata-type conditions ⋮ Approximating fixed points of enriched contractions in Banach spaces ⋮ Generalized contractions for a sequence of multi-valued mappings ⋮ On characterizations of fixed and common fixed points ⋮ Some fixed-circle theorems on metric spaces ⋮ Best proximity points for some classes of proximal contractions ⋮ Common fixed points of compatible maps of type \((\beta)\) on fuzzy metric spaces ⋮ Perturbed geometric contractions in ordered metric spaces ⋮ Meir-Keeler sequential contractions and Pata fixed point results ⋮ On Park's open questions and some fixed-point theorems for general contractive type mappings ⋮ Hölder continuous fractal interpolation functions ⋮ A connection between fixed-point theorems and tiling problems ⋮ Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in \(q\)-uniformly smooth Banach spaces ⋮ Various generalizations of metric spaces and fixed point theorems ⋮ Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces ⋮ An overview of the emergence of weaker continuity notions, various classes of contractive mappings and related fixed point theorems ⋮ Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators ⋮ On fixed points of locally and pointwise contractive set-valued maps with an application to the existence of Nash equilibrium in games ⋮ Fixed points of weakly compatible mappings satisfying generalized \(\varphi\)-weak contractions ⋮ Common fixed point theorems in fuzzy metric spaces ⋮ Existence of strong coupled fixed points for cyclic coupled Ciric-type mappings ⋮ A note on a new class of contractive mappings ⋮ Best proximity points for p-cyclic summing iterated contractions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fixed point results with respect to a wt-distance in partially ordered b-metric spaces and its application to nonlinear fourth-order differential equation ⋮ Fixed point theory for almost convex functions ⋮ Basic Fixed Point Theorems in Metric Spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A Common Fixed Point Theorem for Commuting Mappings ⋮ Some Fixed Point Theorems in Metric Spaces by Altering Distances ⋮ Fixed point theorems for a class of extended JS contraction mappings over a generalized metric space with an application to fixed circle problema ⋮ Common Fixed Point Results on Complex-Valued $S$-Metric Spaces ⋮ Unnamed Item ⋮ Variational Inequality and Complementarity Problem ⋮ A convergence theorem of the sequence of Ishikawa iterates for quasi- contractive mappings ⋮ Some Generalizations of Fixed-Point Theorems on S-Metric Spaces ⋮ Contraction Maps in Pseudometric Structures ⋮ Common fixed point results for mappings of Perov type ⋮ New common fixed point theorems for multivalued maps ⋮ Common fixed point theorems in complete metric and probabilistic metric spaces ⋮ Fixed point theory for cyclic \(\varphi\)-contractions ⋮ Generalized Meir-Keeler type contractions and discontinuity at fixed point ⋮ Some new results on (s,q)-Dass-Gupta-Jaggi type contractive mappings in b-metric-like spaces ⋮ New fixed point results on αψL-rational contraction mappings in metric-like spaces ⋮ Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations ⋮ Best proximity coincidence point theorems for generalized non-linear contraction mappings ⋮ Cyclic \(G\)-\(\Omega \)-weak contraction-weak nonexpansive mappings and some fixed point theorems in metric spaces ⋮ Implicit Contractive Maps in Ordered Metric Spaces ⋮ Unnamed Item ⋮ Firm non-expansive mappings in weak metric spaces ⋮ On the Sum of Contractive Type of Mappings I: Maps on the Same Class ⋮ Interpolative operators: fractal to multivalued fractal ⋮ Weacly Istrǎtescu convex contractions ⋮ Unnamed Item ⋮ Fixed Point Iterations Using Infinite Matrices ⋮ Meir–Keeler Sequential Contractions and Applications ⋮ Survey on Metric Fixed Point Theory and Applications ⋮ Fixed point theorems for simulation functions in $\mbox{b}$-metric spaces via the $wt$-distance ⋮ Contractive definitions and discontinuity at fixed point ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions ⋮ On quasi-contraction mappings of Ćirić and Fisher type via ω-distance ⋮ Set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces ⋮ Graphic Contraction Principle and Applications ⋮ PPF Dependent Fixed Points in Razumikhin Metrical Chains ⋮ Fixed point theorems for contractive mappings and Ciric-Maiti-Pal orbit mappings of contractive type in re-defined generalized metric spaces ⋮ Meir-Keeler theorem in b-rectangular metric spaces ⋮ Weak theta-phi-contraction and discontinuity ⋮ Generalized Z-contraction on quasi metric spaces and a fixed point result ⋮ Some fixed point theorems for single valued strongly contractive mappings in partially ordered ultrametric and non-Archimedean normed spaces ⋮ Nadler-Liu Functional Contractions in Metric Spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fixed point theorems for nonlinear contractions with applications to iterated function systems ⋮ Coincidence points and invariant approximation results for multimaps ⋮ Unnamed Item ⋮ A complete comparison of 25 contraction conditions ⋮ Fixed points of weakly contractive maps and boundedness of orbits ⋮ Fixed points in k complete metric spaces ⋮ Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications ⋮ Common fixed point results for noncommuting mappings without continuity in cone metric spaces ⋮ A fixed point theorem in generalized metric spaces ⋮ A Logical Uniform Boundedness Principle for Abstract Metric and Hyperbolic Spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Stability of iterative procedures with errors for approximating common fixed points of a couple of \(q\)-contractive-like mappings in Banach spaces ⋮ Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space ⋮ Strongly uniform bounds from semi-constructive proofs ⋮ Remarks on fixed point theorems of contractive type ⋮ Unnamed Item ⋮ Some integral type fixed-point theorems and an application to systems of functional equations ⋮ Fixed point results in generalized metric spaces without Hausdorff property ⋮ Quadrupled fixed point results in abstract metric spaces ⋮ A variational principle and best proximity points ⋮ Generalized distance and new fixed point results ⋮ A new contraction principle in Menger spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Random fixed point theorem in probabilistic analysis ⋮ Erratum to the paper “remarks on fixed point theorems of contractive type” ⋮ Remarks on a paper by F. Browder about contraction ⋮ PPF dependent fixed points of generalized contractive type mappings using C-class functions with an application ⋮ Fixed points of mappings over a locally convex topological vector space and Ulam-Hyers stability of fixed point problems ⋮ Fixed point theorem for set-valued mappings with new type of inequalities ⋮ On contractive mappings and discontinuity at fixed points ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Random fixed points for ψ-contractions with application to random differential equations ⋮ Solving existence problems via $F$-contractions ⋮ Fixed point theorem in uniform spaces and applications ⋮ A new Ф-generalized quasi metric space with some fixed point results and applications ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The Retraction-Displacement Condition in the Theory of Fixed Point Equation with a Convergent Iterative Algorithm ⋮ Structural Fixed Point Results in Metric Spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ EXPANSIVE FIXED POINT RESULTS IN SUPER METRIC SPACES ⋮ Some results on \(\mathcal{S}\)-contractions of type \(E\) ⋮ IN Mb v - COMPLETE METRIC SPACE, COMMON FIXED POINT THEOREMS FOR TWO AND FOUR SELF-MAPS UNDER DIFFERENT CONTRACTION PRINCIPLES ⋮ Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences ⋮ Fixed point theorems for cyclic contractions in S-metric spaces involving C-class function ⋮ Fixed points of interpolative Matkowski type contraction and its application in solving non-linear matrix equations ⋮ Connected \(\epsilon\)-chainable sets and existence results ⋮ On φ-contractions and fixed point results in fuzzy metric spaces ⋮ Krasnoselskij-type algorithms for fixed point problems and variational inequality problems in Banach spaces ⋮ Generalized fixed point theorems on metric spaces ⋮ A very general framework for fractal interpolation functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On some new generalizations of Nadler contraction in b-metric spaces ⋮ On W-contractions of Jungck-Ćirić-Wardowski-type in metric spaces ⋮ Fixed point theorems for fuzzy mappings ⋮ Fixed point theorems for fuzzy mappings ⋮ A common fixed point theorem ⋮ Fixed point iterations of three asymptotically pseudocontractive mappings ⋮ Fixed point theorems under Pata-type conditions in metric spaces ⋮ Coincidence best proximity points for geraghty type proximal cyclic contractions ⋮ Some fixed point theorems in Gb-cone metric space ⋮ A NEW NONLINEAR FRACTAL INTERPOLATION FUNCTION ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications ⋮ Unnamed Item ⋮ COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Contractive Operators in Relational Metric Spaces ⋮ Common $e$-soft fixed points of soft set-valued maps ⋮ A remark on asymptotic regularity and fixed point property

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:4141794&oldid=17940941"