• Korean Journal of Mathematics
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• v.13 no.2
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• pp.241-248
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• 2005

Some of the generalized continuous functions and their basic properties are introduced in concern with the cover theory. The open property of a function is a crucial tool for the survey of this area.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.437-442
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• 2014

In this paper we prove Ekeland's variational principle in the setting of locally complete spaces for lower semi continuous functions from above and bounded below. We use this theorem to prove Caristi's fixed point theorem in the same setting and also for lower semi continuous functions.

• Kyungpook Mathematical Journal
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• v.30 no.1
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• pp.95-100
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• 1990

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.535-541
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• 2002

In this paper, we introduce the concept of lower semi-continuous from above functions and show that many well-known results, such as Ekland's and Caristi's theorems, remain also true under lower semi-continuous from above functions.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.229-253
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• 2016

As a generalization of (i, j)-weakly m-continuous functions [43], we introduce the notion of weakly M(i, j)-continuous functions and obtain many characterizations and some properties of the functions. We show that the function is a unified form of some functions between m-spaces and certain kinds of weakly continuous functions in bitopological spaces.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.95-100
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• 1996

In this note, the notion of fuzzy almost s-continuity is introduced and some results related to this notion are obtained.

• The Mathematical Education
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• v.22 no.1
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• pp.31-33
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• 1983

In this paper, we investigate the properties of the semi-continuous functions on the first axiom space, n-th product space, pseudo-metric space, and proximity space. Counterexample is used when the converse of the theorem is not hold.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.493-504
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• 2015

The aim of this paper is to present some properties of sT-continuous functions. Moreover, we obtain a characterization and preserving theorems of semi-compact, S-closed and s-closed spaces.

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1025-1036
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• 2010

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.