• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.127-138
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• 2015

The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying $\phi$-contractive condition.

• Korean Journal of Mathematics
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• v.27 no.3
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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.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.77-84
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• 2012

In this paper, we define the weakly commuting mapping and prove the fixed point theorem for weakly commuting mappings under some conditions on intuitionistic fuzzy metric spaces.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.109-117
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• 2013

In the present paper, we utilize the notion of converse commuting mappings due to L$\ddot{u}$ [On common fixed points for converse commuting self-maps on a metric spaces, Acta. Anal. Funct. Appl. 4(3) (2002), 226-228] and prove a common fixed point theorem in Menger space using an implicit relation. We also give an illustrative example to support our main result.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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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.

• The Pure and Applied Mathematics
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• v.10 no.3
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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.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.411-424
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• 2006

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck's common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem ([21]).

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.257-265
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• 2011

In this paper, we first prove a common fixed point theorem for generalized nonlinear contraction mappings in complete metric spaces there by generalizing and extending some known results. Then we present this result in the context of ordered metric spaces by using monotone non-decreasing mapping.

• East Asian mathematical journal
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• v.22 no.2
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• pp.151-162
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• 2006

In this paper two coincidence point theorems in complete metric spaces for two pairs of single and multi-valued mappings have been established.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.629-645
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• 2010

A metrical common fixed point theorem proved for a pair of self mappings due to Sastry and Murthy ([16]) is extended to symmetric spaces which in turn unifies certain fixed point theorems due to Pant ([13]) and Cho et al. ([4]) besides deriving some related results. Some illustrative examples to highlight the realized improvements are also furnished.