1. Strong Convergence of a New Generalized Viscosity Implicit Rule and Some Applications in Hilbert Space.
- Author
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Postolache, Mihai, Nandal, Ashish, and Chugh, Renu
- Subjects
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HILBERT space , *VARIATIONAL inequalities (Mathematics) , *NONEXPANSIVE mappings , *VISCOSITY , *MONOTONE operators , *POINT set theory , *POINT processes - 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. Symmetry2019, 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. [ABSTRACT FROM AUTHOR] more...
- Published
- 2019
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