On computability and applicability of Mann-Reich-Sabach-type algorithms for approximating the solutions of equilibrium problems in Hilbert spaces

DOI10.1155/2018/7218487zbMath1470.47061OpenAlexW2895647793MaRDI QIDQ1728536

Peter Uche Nwokoro, Felicia Obiageli Isiogugu, Paranjothi Pillay

Publication date: 25 February 2019

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2018/7218487

zbMATH Keywords

fixed pointsstrong convergenceequilibrium problemreal Hilbert spacesbifunctions\(k \)-strictly pseudocontractive-type mappingsmodified Mann-Reich-Sabach iteration scheme

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Strong convergence of a selection of ishikawa-reich-sabach-type algorithm ⋮ On computability and applicability of Mann-Reich-Sabach-type algorithms for approximating the solutions of equilibrium problems in Hilbert spaces ⋮ New iteration scheme for approximating a common fixed point of a finite family of mappings

Cites Work

• Fixed point theory for a class of generalized nonexpansive mappings
• Strong convergence theorems for solving equilibrium problems and fixed point problems of \(\xi \)-strict pseudo-contraction mappings by two hybrid projection methods
• Approximation of a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces
• On computability and applicability of Mann-Reich-Sabach-type algorithms for approximating the solutions of equilibrium problems in Hilbert spaces
• Demiclosedness principle and approximation theorems for certain classes of multivalued mappings in Hilbert spaces
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• Three Strong Convergence Theorems Regarding Iterative Methods for Solving Equilibrium Problems in Reflexive Banach Spaces
• Multivalued Nonexpansive Mappings and Opial's Condition
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