Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces

Ying, Liu; Kong, Hang

doi:10.1007/s13226-019-0373-0

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…(a) Theorem 1 improves, extends, and generalizes the corresponding results [12,13,[30][31][32][33] in the sense that either our method requires an inertial term to improve the convergence rate and/or the space considered is more general. (b) We observe that the result in Corollary 1 improves, and extends the results in [7,[34][35][36] from Hilbert space to a p-uniformly convex and uniformly smooth real Banach space as well as from solving the monotone variational inequality problem to the pseudomonotone variational inequality problem.…”

Section: Remarksupporting

confidence: 57%

Inertial Method for Solving Pseudomonotone Variational Inequality and Fixed Point Problems in Banach Spaces

Maluleka,

Ugwunnadi,

Aphane

2023

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In this paper, we introduce a new iterative method that combines the inertial subgradient extragradient method and the modified Mann method for solving the pseudomonotone variational inequality problem and the fixed point of quasi-Bregman nonexpansive mapping in p-uniformly convex and uniformly smooth real Banach spaces. Under some standard assumptions imposed on cost operators, we prove a strong convergence theorem for our proposed method. Finally, we perform numerical experiments to validate the efficiency of our proposed method.

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Section: Remarksupporting

confidence: 57%

Inertial Method for Solving Pseudomonotone Variational Inequality and Fixed Point Problems in Banach Spaces

Maluleka,

Ugwunnadi,

Aphane

2023

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Fast hybrid method for solving variational inequalities beyond monotonicity in real Banach spaces

Uzor,

Mewomo,

Gibali

2024

Optimization

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A new system of generalized nonlinear variational inclusion problems in semi-inner product spaces

Shafi

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this work we reflect a new system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. By using resolvent operator technique, we offer an iterative algorithm for figuring out the approximate solution of the said system. The motive of this paper is to review the convergence analysis of a system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. The proposition used in this paper can be considered as an extension of propositions for examining the existence of solution for various classes of variational inclusions considered and studied by many authors in 2-uniformly smooth Banach spaces.

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Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces

Cited by 4 publications

References 22 publications

Inertial Method for Solving Pseudomonotone Variational Inequality and Fixed Point Problems in Banach Spaces

Inertial Method for Solving Pseudomonotone Variational Inequality and Fixed Point Problems in Banach Spaces

Fast hybrid method for solving variational inequalities beyond monotonicity in real Banach spaces

A new system of generalized nonlinear variational inclusion problems in semi-inner product spaces

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