• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.225-232
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• 2003

In this paper, we consider the existence of the solutions to the generalized vector variational-type inequalities for set-valued mappings on Hausdorff topological vector spaces using Fan's geometrical lemma.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.848-851
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• 2010

In this paper, we introduce the concept of fuzzy quasi topologies which are generalizations of smooth topologies and Chang's fuzzy topologies, and obtain some basic properties of their structures.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.255-270
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• 2007

In this paper, we introduce the concepts of r-generalized fuzzy closed sets, r-generalized fuzzy continuous maps and several types of r-generalized compactness in fuzzy topological spaces and investigate some of their properties.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.883-894
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• 2021

The aim of this work is to introduce for the first time the concept of D-set. This is done by defining a special type of cover called a D-cover. we present some results to study the properties of D-compact spaces and their relations with other topological spaces. Several examples are discussed to illustrate and support our main results. Our results extend and generalized many will known results in the literature.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.163-169
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• 2011

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.809-813
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• 2012

We introduce the notion of R($g$, $g^{\prime}$)-continuity on generalized topological spaces, which is a strong form of ($g$, $g^{\prime}$)-continuity. We investigate some properties and relationships among R($g$, $g^{\prime}$)-continuity, ($g$, $g^{\prime}$)-continuity and some strong forms of ($g$, $g^{\prime}$)-continuity.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.129-130
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• 2008

In this paper, we introduce the concept of generalized fuzzy (r,s)-closed sets on intuitionistic fuzzy topological spaces in ${\v{S}ostak's$ sense. Using this concept, we introduce the notions of generalized fuzzy (r,s)-continuous mappings, and then we investigate some of their properties.

• East Asian mathematical journal
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• v.26 no.1
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.537-545
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• 2007

Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in the setup of certain metrizable topological vector spaces are obtained. As applications, related results on best approximation are derived. Our results extend, generalize and unify various known results in the literature.