Generalized Projection Operators in Banach Spaces: Properties and Applications
From MaRDI portal
Publication:5689992
zbMath0882.47046arXivfunct-an/9311002MaRDI QIDQ5689992
Publication date: 15 January 1997
Full work available at URL: https://arxiv.org/abs/funct-an/9311002
variational inequalitygeneralized projection operatorsiterative-projection methodcommon point of convex setsmetric projection operators in Banach space
Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Nonlinear accretive operators, dissipative operators, etc. (47H06) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)
Related Items
A halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces ⋮ Proximal projection methods for variational inequalities and Cesáro averaged approximations ⋮ Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces. ⋮ Iterative construction of fixed points of nonself-mappings in Banach spaces ⋮ Calculus rules for \(V\)-proximal subdifferentials in smooth Banach spaces ⋮ A convergence theorem for solving generalized mixed equilibrium problems and finding fixed points of a weak Bregman relatively nonexpansive mappings in Banach spaces ⋮ Generalised-prox-regularity in reflexive smooth Banach spaces with smooth dual norm ⋮ On systems of generalized nonlinear variational inequalities in Banach spaces ⋮ Solvability of \(f\)-complementarity problems with a new exceptional family of elements ⋮ The connection between the metric and generalized projection operators in Banach spaces ⋮ Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces ⋮ Convergence of Bregman projection methods for solving consistent convex feasibility problems in reflexive Banach spaces ⋮ Approximation of common solutions of nonlinear problems in Banach spaces ⋮ A common solution of generalized equilibrium, zeros of monotone mapping and fixed point problems ⋮ A generalized \(f\)-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities ⋮ Operator-theoretic and regularization approaches to ill-posed problems ⋮ Iterative schemes for nonconvex quasi-variational problems with \(V\)-prox-regular data in Banach spaces ⋮ \(W\)-approximative compactness and continuity of the generalized projection operator in Banach spaces ⋮ Shrinking projection algorithms for equilibrium problems with a bifunction defined on the dual space of a Banach space ⋮ A modified Mann iterative scheme by generalized \(f\)-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems ⋮ A generalized self-adaptive algorithm for the split feasibility problem in Banach spaces ⋮ The best approximation theorems and fixed point theorems for discontinuous increasing mappings in Banach spaces ⋮ Convex sweeping processes with noncompact perturbations and with delay in Banach spaces ⋮ Strong convergence of a generalized forward–backward splitting method in reflexive Banach spaces ⋮ Convergence theorems for modified generalized \(f\)-projections and generalized nonexpansive mappings ⋮ A Mann type hybrid generalized \(f\)-projection iterative method for a class of nonlinear mappings ⋮ A strong convergence theorem for relatively nonexpansive mappings and equilibrium problems in Banach spaces ⋮ Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications ⋮ Mann-type algorithms for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces ⋮ Weak and strong convergence results for solving monotone variational inequalities in reflexive Banach spaces ⋮ Forward-reflected-backward splitting method without cocoercivity for the sum of maximal monotone operators in Banach spaces ⋮ Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces ⋮ Implicit second order differential inclusions in reflexive smooth Banach spaces ⋮ Smooth over-parameterized solvers for non-smooth structured optimization ⋮ Novel inertial methods for fixed point problems in reflexive Banach spaces with applications ⋮ Degree theory for a generalized set-valued variational inequality with an application in Banach spaces ⋮ Algorithms for Nonlinear Integral Equations of Hammerstein Type with Phi-monotone Mappings in Certain Banach Spaces ⋮ Approximating properties of metric and generalized metric projections in uniformly convex and uniformly smooth Banach spaces ⋮ A first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space ⋮ Projection algorithms for the system of mixed variational inequalities in Banach spaces ⋮ Approximation of fixed points of weak Bregman relatively nonexpansive mappings in Banach spaces ⋮ Strong convergence theorems for countable families of uniformly quasi-\(\phi\)-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems ⋮ Existence and algorithm for solving the system of mixed variational inequalities in Banach spaces ⋮ Unbounded state-dependent sweeping processes with perturbations in uniformly convex and \(q\)-uniformly smooth Banach spaces ⋮ State dependent sweeping process in \(p\)-uniformly smooth and \(q\)-uniformly convex Banach spaces ⋮ The modified Mann type iterative algorithm for a countable family of totally quasi-\(\phi\)-asymptotically nonexpansive mappings by the hybrid generalized f-projection method ⋮ Nonlinear iterative methods for solving the split common null point problem in Banach spaces ⋮ The generalized \(f\)-projection operator and set-valued variational inequalities in Banach spaces ⋮ A generalized \(f\)-projection algorithm for inverse mixed variational inequalities ⋮ Noncompact perturbation of sweeping process with delay in Banach spaces ⋮ \(V\)-prox-regular functions in smooth Banach spaces ⋮ A new system of multivalued mixed variational inequality problem ⋮ Existence theorems for variational inequalities in Banach spaces ⋮ Generalized projections on closed nonconvex sets in uniformly convex and uniformly smooth Banach spaces ⋮ Properties of the generalized \(f\)-projection operator and its applications in Banach spaces ⋮ A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings ⋮ Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings ⋮ A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces ⋮ Iterative schemes for approximating solution of nonlinear operators in Banach spaces ⋮ Strong convergence of shrinking projection methods for quasi-nonexpansive mappings and equilibrium problems ⋮ Projection algorithms for the system of generalized mixed variational inequalities in Banach spaces ⋮ On the convergence of hybrid projection algorithms for asymptotically quasi-\(\phi\)-nonexpansive mappings ⋮ Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces ⋮ Convergence theorems of shrinking projection methods for equilibrium problem, variational inequality problem and a finite family of relatively quasi-nonexpansive mappings ⋮ On hybrid projection methods for asymptotically quasi-\(\phi\)-nonexpansive mappings ⋮ An iterative shrinking metric \(f\)-projection method for finding a common fixed point of a closed and quasi-strict \(f\)-pseudocontraction and a countable family of firmly nonexpansive mappings and applications in Hilbert spaces ⋮ The generalized projection operator on reflexive Banach spaces and its applications ⋮ Proximal analysis in reflexive smooth Banach spaces ⋮ State dependent nonconvex sweeping processes in smooth Banach spaces ⋮ Existence theorem and algorithm for a general implicit variational inequality in Banach space ⋮ On the generalized Bregman projection operator in reflexive Banach spaces ⋮ Existence result and error bounds for a new class of inverse mixed quasi-variational inequalities ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On some algorithms in Banach spaces finding fixed points of nonlinear mappings ⋮ Bregman distance and strong convergence of proximal-type algorithms ⋮ An iterative method with residual vectors for solving the fixed point and the split inclusion problems in Banach spaces ⋮ The monotone contraction mapping theorem ⋮ A shrinking projection algorithm with errors for Costerro bounded linear mappings ⋮ Ill-Posed Problems: Operator Methodologies of Resolution and Regularization ⋮ Existence results for second order nonconvex sweeping processes in \(q\)-uniformly convex and 2-uniformly smooth separable Banach spaces ⋮ The regularization method for variational inequalities with nonsmooth unbounded operators in Banach space