Viscosity Self-Adaptive Method for Generalized Split System of Variational Inclusion Problem

Abstract

In this paper, we propose a viscosity-type and self-adaptive iterative algorithm resulting in strong convergence theorem for finding the common solution of generalized split system of variational inclusion problem. The self-adaptive technique presented in this paper is a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. As an application of our result, we study the strong convergence theorem to approximate the solution of generalized forms of multiple-set split feasibility problem, split system of equilibrium problem and split system of minimization problem. Our result generalize, improve and unify various results in the existing literature.

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Correspondence to Anteneh Getachew Gebrie.

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Communicated by Behzad Djafari-Rouhani.

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Gebrie, A.G., Bekele, B. Viscosity Self-Adaptive Method for Generalized Split System of Variational Inclusion Problem. Bull. Iran. Math. Soc. (2020). https://doi.org/10.1007/s41980-020-00418-1

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Keywords

  • Variational inclusion problem
  • Firmly nonexpansive mapping
  • Viscosity method
  • Self-adaptive stepsize

Mathematics Subject Classification

  • 90C25
  • 65K05
  • 47J20
  • 47H05