• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.319-323
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• 2001

First, we study some properties of F-continuities. Second, we introduce the concept of fuzzy set-valued mappings and study some properties of fuzzy set-valued mappings and fuzzy set-valued continuous mappings. Finally, we Introduce the concept of fuzzy semi-continuous of fuzzy set-valued mappings and investigate their some properties.

• East Asian mathematical journal
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• v.24 no.4
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• pp.339-345
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• 2008

Some equivalence conditions for the convergence of iterative sequences for set-valued contraction mapping in Banach spaces are obtained.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.439-454
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• 2013

In this paper, we introduce the Birkho integral of fuzzy mappings in Banach spaces in terms of the Birkhoff integral of set-valued mappings and investigate some properties of the Birkho integrals of set-valued mappings and fuzzy mappings in Banach spaces.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.381-393
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• 2012

In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

• 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.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.277-286
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• 2003

In this paper, the Monger Probabilistic n-metric space is presented, some Hex point theorem for set valued mapping are extended to Monger probabilistic n-metric space.

• 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.

• 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.