Strongly convergent iterative methods for split equality variational inclusion problems in banach spaces

“…In 2015, Takahashi [19] introduced and studied the common null point problem in Banach spaces. Also in 2016, Chang et al [2] introduced and studied the split equality variational inclusion problems in the setting of Banach spaces. Motivated by the above works and related literatures, the purpose of this paper is to introduce and study the so-called split equality quasi inclusion problems for accretive and the m-accretive mappings in Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces

Chang¹,

Wen²,

Yao³

et al. 2017

J. Nonlinear Sci. Appl.

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A generalized forward-backward method for solving split equality quasi inclusion problems of accretive operators in Banach spaces is studied. Some strong convergence theorems for the sequences generalized by the algorithm to a solution of quasi inclusion problems of accretive operators are proved under certain assumptions. The results presented in this paper are new which extend and improve the corresponding results announced in the recent literatures. At the end of the paper some applications to monotone variational inequalities, convex minimization problem, and convexly constrained linear inverse problem are presented. c 2017 All rights reserved.Keywords: Generalized forward-backward method, accretive operator, m-accretive operator, maximal monotone operator, split equality quasi inclusion problem. 2010 MSC: 47H09, 47H10, 47N10.

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“…In 2016, Chang et al (2016) introduced and studied the split equality variational inclusion problems in the setting of Banach spaces. The split equality variational inclusion problem (SEVIP) is defined as follows:…”

Section: Introductionmentioning

confidence: 99%

“…Here, H i , i = 1, 2 are real Hilbert spaces and X is a real Banach space. If we consider X = H 3 , where H 3 is a real Hilbert space, then the main result of Chang et al (2016) will be as follows.…”

Section: Introductionmentioning

confidence: 99%

Application of new strongly convergent iterative methods to split equality problems

et al. 2020

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In this paper, we study the generalized problem of split equality variational inclusion problem. For this purpose, we introduced the problem of finding the zero of a nonnegative lower semicontinuous function over the common solution set of fixed point problem and monotone inclusion problem. We proposed and studied the convergence behaviour of different iterative techniques to solve the generalized problem. Furthermore, we study an inertial form of the proposed algorithm and compare the convergence speed. Numerical experiments have been conducted to compare the convergence speed of the proposed algorithm, its inertial form and already existing algorithms to solve the generalized problem. Keywords Split equality problem • Variational inclusion problem • Fixed point problem • Quasi-nonexpansive mapping Mathematics Subject Classification 47J25 • 47H05 • 47H09 • 49J53 Communicated by Ernesto G. Birgin.

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Strongly convergent iterative methods for split equality variational inclusion problems in banach spaces

Cited by 17 publications

References 18 publications

On solving general split equality variational inclusion problems in Banach space

On solving general split equality variational inclusion problems in Banach space

A generalized forward-backward method for solving split equality quasi inclusion problems in Banach spaces

Application of new strongly convergent iterative methods to split equality problems

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