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CONVERGENCE AND STABILITY OF ITERATIVE ALGORITHM OF SYSTEM OF GENERALIZED IMPLICIT VARIATIONAL-LIKE INCLUSION PROBLEMS USING (θ,φ,γ)-RELAXED COCOERCIVITY
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Type
Academic journal
Author
Jong Kyu Kim (Kyungnam University) Mohd Iqbal Bhat (University of Kashmir South Campus) Sumeera Shafi (NIT Srinagar)
Journal
경남대학교 기초과학연구소 Nonlinear Functional Analysis and Applications Nonlinear Functional Analysis and Applications Vol.26 No.4 KCI Accredited Journals
Published
2021.12
Pages
749 - 780 (32page)
DOI
10.22771/nfaa.2021.26.04.07

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CONVERGENCE AND STABILITY OF ITERATIVE ALGORITHM OF SYSTEM OF GENERALIZED IMPLICIT VARIATIONAL-LIKE INCLUSION PROBLEMS USING (θ,φ,γ)-RELAXED COCOERCIVITY
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In this paper, we give the notion of $M(.,.)$-$\eta$-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of $M(.,.)$-$\eta$-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.
#Variational-like inclusion #$M(. #.)$-$eta$-proximal mapping #$0$-diagonally quasi-concave #iterative algorithm #convergence and stability.

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S. Adly / 1996 / Perturbed algorithms and sensitivity analysis for a general class of variational inclusions / J. Math. Anal. Appl 201:609~630 google schola C. Baiocchi / 1984 / Variational and Quasi-variational Inequalities: Applications to Free Boundary Problems / John Wiley and Sons google schola Mohd Iqbal Bhat / 2021 / H-mixed accretive mapping and proximal point method for solving a system of generalized set-Valued variational inclusions / Numerical Functional Analysis and Optimization 42(8):955~972 Crossref Mohd Bhat / 2017 / Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces / Filomat 31(19):6051~6070 Crossref M. I. Bhat / 2017 / (H(·, ·), η)-monotone operators with an application to a system of set-valued variational-like inclusions in Banach spaces / Nonlinear Funct. Anal. Appl 22(3):673~692 google schola

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