• 충청수학회지
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• 제23권3호
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• pp.589-598
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• 2010

Generalizing normally quasi-ordered spaces, we introduce a concept of regularly quasi-ordered spaces and study their categorical properties. We obtain well behaved reflective subcategories of the category Rqos of regularly quasi-ordered spaces and continuous isotones, namely the full subcategory of Rqos determined by $T_0$-objects among others, and this result can be extended to that in the category Nqos of normally quasi-ordered spaces and continuous isotones.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권1호
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• pp.25-35
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• 2003

We study equivalent definitions and some categorical properties of completely regular quasi-ordered spaces and zero-dimensional quasi-ordered spaces. Using the o-completely regular (resp. o-zero-dimensional) filters on a completely regular (resp. zero-dimensional) quasi-ordered space, we show that the category COMPOS (resp. ZCOMPOS) of compact (resp. compact zero-dimensional) partially ordered spaces is reflective in the category CRQOS (resp. ZQOS) of completely regular (resp. zero-dimensional) quasi-ordered spaces and continuous isotones.

• 대한수학회논문집
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• 제17권4호
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• pp.681-691
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• 2002

We study categorical properties of the category SWQOS (S$\^$U/WQOS, S$\^$L/WQOS, resp) of (upper, lower, resp.) semi-continuous quasi-ordered spaces and the subcategory SWPOS (S$\^$U/WPOS, S$\^$L/WPOS, resp.) of (upper, lower, resp.) semicontinuous partially ordered spaces. We show that the categories S$\^$U/WPOS, S$\^$L/WPOS and SWPOS are closed under the formation of initial mono-sources in the category TQOS of topological quasi-ordered spaces, and they we mono-topological, complete and cocomplete epireflective subcategories of the category TQOS. We obtain their MacNeille and universal initial completions, as well as those of subcatego.ies S$\^$U/WQOS(S$\^$L/WQOS) and SWQOS, in which the topologies are T$\_$0/ and T$_1$, respectively.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.361-370
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• 2002

We are to present some properties of binary relations on fuzzy topological spares by means of categorical method. The concept of fuzzy topological ordered spaces was introduced by Katsaras[8]. In this paper we study some special categories, i.e, FTQOS, FTPOS, LSCQ, USCQ, SCQ, CQ, NQO, CRQO, associated with fuzzy topological spaces.

• 대한수학회논문집
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• 제27권1호
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.93-104
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• 2024

In this paper, we will prove a fixed point theorem for self-mappings on a generalized quasi-ordered metric space which is a generalization of the concept of a generalized metric space with a partial order and we investigate a genralized quasi-ordered metric space related with fuzzy normed spaces. Further, we prove the stability of some functional equations in fuzzy normed spaces as an application of our fixed point theorem.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.169-179
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• 2016

In this article, we introduce the concept of ordered dualistic partial metric spaces and establish an order relation on quasi dualistic partial metric spaces. Later on, using this order relation, we prove xed point theorems for single and multivalued mappings. We support our results with some illustrative examples.

• Kyungpook Mathematical Journal
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• 제20권2호
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• pp.145-158
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• 1980

• Kyungpook Mathematical Journal
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• 제31권2호
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• pp.235-241
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• 1991