A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

doi:10.23952/jnfa.2020.37

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…The SFP is known to have useful applications in many fields such as phase retrieval, medical image reconstruction, radiation therapy treatment planning, signal processing, among others, see [1,15,36]. In 2003, Byrne [13] in the framework of Euclidean spaces proposed a CQ algorithm of the form…”

Section: Introductionmentioning

confidence: 99%

On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces

et al. 2022

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In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also a fixed point of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We display a numerical example to illustrate the performance of our result. The result presented in this article unifies and extends several existing results in the literature.

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Section: Introductionmentioning

confidence: 99%

On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces

et al. 2022

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A Modified inertial Halpern method for solving split monotone variational inclusion problems in Banach Spaces

Abass

Ugwunnadi

Narain

2022

Rend. Circ. Mat. Palermo, II. Ser

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An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

Oyewole

2021

Demonstratio Mathematica

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In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi- ϕ \phi -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E 1 {E}_{1} and a smooth, strictly convex and reflexive Banach space E 2 {E}_{2} . Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.

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A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

Cited by 4 publications

References 14 publications

On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces

On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces

A Modified inertial Halpern method for solving split monotone variational inclusion problems in Banach Spaces

An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

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