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

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Résumé

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.

langueAnglais
Pages983-998
Nombre de pages16
journalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume111
Numéro4
Les DOIs
étatPublié - 1 oct. 2017

Empreinte digitale

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

mots-clés

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    title = "Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space",
    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",
    author = "Giang, {Dinh Minh} and Strodiot, {Jean Jacques} and Nguyen, {Van Hien}",
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    T1 - Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space

    AU - Giang,Dinh Minh

    AU - Strodiot,Jean Jacques

    AU - Nguyen,Van Hien

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    AB - 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.

    KW - Demiclosed operator

    KW - Multiple-set split equality fixed point problem

    KW - Quasi-nonexpansive operator

    KW - Strong convergence

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    T2 - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

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