• Title, Summary, Keyword: Set-valued mapping

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A RESOLVENT APPROACH FOR SOLVING A SET-VALUED VARIATIONAL INCLUSION PROBLEM USING WEAK-RRD SET-VALUED MAPPING

  • Ahmad, Iqbal;Ahmad, Rais;Iqbal, Javid
    • Korean Journal of Mathematics
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    • v.24 no.2
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    • pp.199-213
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    • 2016
  • The resolvent operator approach of [2] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.

SYSTEM OF GENERALIZED SET-VALUED PARAMETRIC ORDERED VARIATIONAL INCLUSION PROBLEMS WITH OPERATOR ⊕ IN ORDERED BANACH SPACES

  • Akram, Mohammad;Dilshad, Mohammad
    • Communications of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.103-119
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    • 2021
  • In this article, we study a system of generalized set-valued parametric ordered variational inclusion problems with operator ⊕ in ordered Banach spaces. We introduce the concept of the resolvent operator associated with (α, λ)-ANODSM set-valued mapping and establish the existence theorem of solution for the system of generalized set-valued parametric ordered variational inclusion problems in ordered Banach spaces. In order to prove the existence of solution, we suggest an iterative algorithm and discuss the convergence analysis under some suitable mild conditions.

A SYSTEM OF NONLINEAR SET-VALUED IMPLICIT VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuanzhi;Yang, Qing
    • Communications of the Korean Mathematical Society
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    • v.25 no.1
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    • pp.129-137
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    • 2010
  • In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

CONVERGENCE THEOREMS FOR SET-VALUED DENJOY-PETTIS INTEGRABLE MAPPINGS

  • Park, Chun-Kee
    • Communications of the Korean Mathematical Society
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    • v.24 no.2
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    • pp.227-237
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    • 2009
  • In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued Denjoy-Pettis integrable mappings.

MODIFIED ISHIKAWA ITERATIVE SEQUENCES WITH ERRORS FOR ASYMPTOTICALLY SET-VALUED PSEUCOCONTRACTIVE MAPPINGS IN BANACH SPACES

  • Kim, Jong-Kyu;Nam, Young-Man
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.847-860
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    • 2006
  • In this paper, some new convergence theorems of the modified Ishikawa and Mann iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in uniformly smooth Banach spaces are given.

FIXED POINT AND PERIODIC POINT THEOREMS ON METRIC SPACES

  • Cho, Seong-Hoon;Park, Dong-Gon
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.1
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    • pp.1-16
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    • 2013
  • The aim of this paper is to establish a new fixed point theorem for a set-valued mapping defined on a metric space satisfying a weak contractive type condition and to establish a new common fixed point theorem for a pair of set-valued mappings defined on a metric space satisfying a weak contractive type inequality. And we give periodic point theorems for single-valued mappings defined on a metric space satisfying weak contractive type conditions.

T-FUZZY INTEGRALS OF SET-VALUED MAPPINGS

  • CHO, SUNG JIN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.1
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    • pp.39-48
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    • 2000
  • In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.

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