Approximation of the common minimum-norm fixed point of a finite family of asymptotically nonexpansive mappings

DOI10.1186/1687-1812-2013-1zbMath1423.47055OpenAlexW2104128462WikidataQ59294701 ScholiaQ59294701MaRDI QIDQ395236

Mohammad Hasan, H. S. Yoon

Publication date: 29 January 2014

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2013-1

zbMATH Keywords

strong convergencenonexpansive mappingssplit feasibility problemasymptotically nonexpansive mappingsminimum-norm fixed point

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

\(S_H\)-metric spaces and fixed-point theorems for multi-valued weak contraction mappings ⋮ STRONG CONVERGENCE THEOREM OF A VISCOSITY PROCESS FOR A FINITE FAMILY OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS ⋮ Application of the fixed point theorems on the existence of solutions for \(q\)-fractional boundary value problems ⋮ Fixed point results for dominated mappings in rectangular \(b\)-metric spaces with applications ⋮ Fractional convex type contraction with solution of fractional differential equation ⋮ Common fixed point results for couples \((f,g)\) and \((S,T)\) satisfy strong common limit range property ⋮ Deferred statistical convergence of order \(\alpha\) in metric spaces ⋮ Approximating a common point of fixed points of a pseudocontractive mapping and zeros of sum of monotone mappings ⋮ An iteration process for a general class of contractive-like operators: convergence, stability and polynomiography ⋮ The Meir-Keeler type contractions in extended modular \(b\)-metric spaces with an application ⋮ Fixed point results in double controlled quasi metric type spaces ⋮ Bipolar soft functions ⋮ Soft \(\alpha \)-separation axioms and \(\alpha \)-fixed soft points ⋮ A modified Picard S-hybrid iterative process for solving split generalized equilibrium problem ⋮ Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application ⋮ On fixed point theorems for a class of \(\alpha\)-\(\hat{v}\)-Meir-Keeler-type contraction mapping in modular extended \(b\)-metric spaces ⋮ An algorithm with general errors for the zero point of monotone mappings in Banach spaces ⋮ High-order sum-of-squares structured tensors: theory and applications ⋮ Fixed points of nonlinear contractions with applications ⋮ Bivariate general Appell interpolation problem ⋮ Ulam-Hyers Stability of Functional Equations in Quasi-β-Banach Spaces ⋮ Approximations for equilibrium problems and nonexpansive semigroups ⋮ Implicit approximation scheme for the solution of \(K\)-positive definite operator equation ⋮ Local fractional derivative boundary value problems for Tricomi equation arising in fractal transonic flow ⋮ Approximation of minimum-norm fixed point of total asymptotically nonexpansive mapping ⋮ A general iterative algorithm for an infinite family of nonexpansive operators in Hilbert spaces ⋮ Fixed points of Edelstein-type multivalued maps ⋮ Another type of Mann iterative scheme for two mappings in a complete geodesic space ⋮ Viscosity approximations considering boundary point method for fixed-point and variational inequalities of quasi-nonexpansive mappings ⋮ Strong convergence of approximated iterations for asymptotically pseudocontractive mappings ⋮ On the iterates of asymptotically \(k\)-strict pseudocontractive mappings in Hilbert spaces with convergence analysis ⋮ Fixed points of \((\varphi,F)\)-weak contractions on metric-like spaces with applications to integral equations on time scales ⋮ Several iterative algorithms for solving the split common fixed point problem of directed operators with applications ⋮ Smoothness of Orlicz function spaces equipped with the \(p\)-Amemiya norm ⋮ Strong convergence result of split feasibility problems in Banach spaces ⋮ Some fixed point theorems in Gb-cone metric space

Cites Work

• Unnamed Item
• Unnamed Item
• Finding minimum norm fixed point of nonexpansive mappings and applications
• Iterative construction of fixed points of asymptotically nonexpansive mappings
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• On Reich's strong convergence theorems for resolvents of accretive operators
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Strong convergence of averaged approximants for asymptotically nonexpansive mappings in Banach spaces
• A strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces
• A multiprojection algorithm using Bregman projections in a product space
• Iterative approaches to convex feasibility problems in Banach spaces
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• A hybrid iteration scheme for equilibrium problems, variational inequality problems and common fixed point problems in Banach spaces
• Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces
• Fixed point theorems for asymptotically nonexpansive mappings
• Fixed Point Iteration Processes for Asymptotically Nonexpansive Mappings
• Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
• Convergence of paths for pseudo-contractive mappings in Banach spaces
• Iterative oblique projection onto convex sets and the split feasibility problem
• Fixed points of nonexpanding maps
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings