Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space

Research output: Contribution to journalArticle

Abstract

In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.

Original languageEnglish
Pages (from-to)983-998
Number of pages16
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume111
Issue number4
DOIs
Publication statusPublished - 1 Oct 2017

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Fixed Point Problem
Hilbert spaces
Iterative methods
Strong Convergence
Equality
Hilbert space
Iteration
Multivalued Mapping
Operator Norm
Fixed Point Set
Projection Operator
Multivalued
Nonexpansive Mapping
Convex function
Differentiable
Mathematical operators
Intersection
Projection
Family

Keywords

  • Demiclosed operator
  • Multiple-set split equality fixed point problem
  • Quasi-nonexpansive operator
  • Strong convergence

Cite this

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abstract = "In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.",
keywords = "Demiclosed operator, Multiple-set split equality fixed point problem, Quasi-nonexpansive operator, Strong convergence",
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