Strong Convergence of a New Generalized Viscosity Implicit Rule and Some Applications in Hilbert Space

Mihai Postolache, Ashish Nandal and Renu Chugh
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Mihai Postolache: Department of General Education, China Medical University, Taichung 40402, Taiwan
Ashish Nandal: Department of Mathematics, Pt NRS Government College, Rohtak 124001, India
Renu Chugh: Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India

Mathematics, 2019, vol. 7, issue 9, 1-24

Abstract: In this paper, based on the very recent work by Nandal et al. (Nandal, A.; Chugh, R.; Postolache, M. Iteration process for fixed point problems and zeros of maximal monotone operators. Symmetry 2019 , 11 , 655.), we propose a new generalized viscosity implicit rule for finding a common element of the fixed point sets of a finite family of nonexpansive mappings and the sets of zeros of maximal monotone operators. Utilizing the main result, we first propose and investigate a new general system of generalized equilibrium problems, which includes several equilibrium and variational inequality problems as special cases, and then we derive an implicit iterative method to solve constrained multiple-set split convex feasibility problem. We further combine forward-backward splitting method and generalized viscosity implicit rule for solving monotone inclusion problem. Moreover, we apply the main result to solve convex minimization problem.

Keywords: generalized viscosity implicit rule; zero point; fixed point; system of generalized equilibrium problems; constrained multiple-set split convex feasibility problem; monotone inclusion problem; minimization problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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