• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권3호
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• 대한수학회논문집
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• 제27권3호
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• pp.513-522
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• 2012

In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.629-643
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• 2019

In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.591-603
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• 2008

We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result.

• 대한수학회보
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• 제34권2호
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

• 대한수학회보
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• 제47권3호
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• pp.503-511
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• 2010

We prove a common fixed point theorem for S-contraction mappings without continuity. Using this result we obtain an approximating curve for S-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for S-nonexpansive mappings is also established.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.165-181
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• 2014

We establish a common n-tupled fixed point theorem for hybrid pair of mappings under new contractive condition. It is to be noted that to find n-tupled coincidence point, we do not use the condition of continuity of any mapping involved. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.135-151
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• 2008

The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on non complete Menger spaces. Our results extend, improve and generalize several known results in Menger spaces. We give formulas for total number of commutativity conditions for finite number of mappings.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.23-38
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• 2014

In this paper, we introduce the concept of w¡compatibility and weakly commutativity for hybrid pair of mappings $F:X{\times}X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$ and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권3호
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• pp.199-214
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• 2015

We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.