Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications

DOI10.1016/j.camwa.2010.06.013zbMath1201.65091OpenAlexW1973540418MaRDI QIDQ611463

Donal O'Regan, Nan-Jing Huang, Xi Li

Publication date: 14 December 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.06.013

zbMATH Keywords

nonexpansive mappinggeneralized \(f\)-projection operatorrelatively nonexpansive mappingasymptotic fixed pointgeneral \(H\)-monotone mapping

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Convergence theorems for equilibrium problem and asymptotically quasi-\(\phi\)-nonexpansive mappings in the intermediate sense, An iterative method for total quasi-\(\phi\)-asymptotically nonexpansive semi-groups and generalized mixed equilibrium problems in Banach spaces, A generalized \(f\)-projection method for countable families of weak relatively nonexpansive mappings and the system of generalized Ky Fan inequalities, 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 modified two-layer iteration via a boundary point approach to generalized multivalued pseudomonotone mixed variational inequalities, 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 a common fixed point of two countable families of relatively quasi nonexpansive mappings and applications, A new iterative scheme for a countable family of relatively nonexpansive mappings and an equilibrium problem in Banach spaces, The approximation of common element for maximal monotone operator, generalized mixed equilibrium problem and fixed point problem, Convergence theorems by hybrid method for systems of equilibrium problems and fixed point problem, A new iterative scheme for countable families of weak relatively nonexpansive mappings and system of generalized mixed equilibrium problems, Halpern-type iterations for strongly relatively nonexpansive mappings in Banach spaces, Strong convergence theorems for infinite family of relatively quasi nonexpansive mappings and systems of equilibrium problems, Strong convergence theorems for countable families of uniformly quasi-\(\phi\)-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems, A Halpern-Mann type iteration for fixed point problems of a relatively nonexpansive mapping and a system of equilibrium problems, Hybrid iterative scheme for fixed point problem, infinite systems of equilibrium and variational inequality problems, The modified Mann type iterative algorithm for a countable family of totally quasi-\(\phi\)-asymptotically nonexpansive mappings by the hybrid generalized f-projection method, Bregman \(f\)-projection operator with applications to variational inequalities in Banach spaces, Measure theory and \(S^2\)-pseudo almost periodic and automorphic process: application to stochastic evolution equations, Iterative approximation of countable family of relatively nonexpansive mappings and system of equilibrium problems in Banach spaces, Projection methods for a system of nonlinear mixed variational inequalities in Banach spaces, Existence results for trifunction equilibrium problems and fixed point problems, Iterative schemes for approximating solution of nonlinear operators in Banach spaces, A modified Halpern-type iterative method of a system of equilibrium problems and a fixed point for a totally quasi-\(\phi\)-asymptotically nonexpansive mapping in a Banach space, Strong convergence theorems for families of weak relatively nonexpansive mappings, Hybrid algorithms for equilibrium and common fixed point problems with applications, Convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems, Uniformly closed replaced AKTT or \({^{\ast}\mathrm{AKTT}}\) condition to get strong convergence theorems for a countable family of relatively quasi-nonexpansive mappings and systems of equilibrium problems, A new hybrid iterative scheme for countable families of relatively quasi-nonexpansive mappings and system of equilibrium problems, 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, Strong convergence theorems for fixed point problems of infinite family of asymptotically quasi-\(\phi\)-nonexpansive mappings and a system of equilibrium problems, 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, The hybrid projection algorithm for finding the common fixed points of nonexpansive mappings and the zeroes of maximal monotone operators in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• A strong convergence theorem for relatively nonexpansive mappings in a Banach space
• The generalized \(f\)-projection operator and set-valued variational inequalities in Banach spaces
• Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Variational inclusions with a general \(H\)-monotone operator in Banach spaces
• Properties of the generalized \(f\)-projection operator and its applications in Banach spaces
• Strong Convergence of a Proximal-Type Algorithm in a Banach Space
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• The generalised f-projection operator with an application
• Generalized Projection Operators in Banach Spaces: Properties and Applications