• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.245-254
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• 2003

In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].

• 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.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.607-614
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• 2008

We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.551-564
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• 2013

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive selfmaps and invariant approximations, Acta Math. Sinica, 24(5) (2008), 867-876] introduced the notion of occasionally weakly compatible mappings in metric spaces. In this paper, we prove some common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using an implicit relation. We also give an illustrative example to support our main result.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.115-126
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• 2017

In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.455-466
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• 2021

Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in G-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.393-409
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• 2021

Three common fixed point theorems for weakly compatible mappings satisfying three classes of contractive inequalities of integral type are proved. Three examples are included. The results obtained in this paper extend and improve a few results existing in literature.

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.133-144
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• 2003

The aim of this paper is to prove some common fixed point theorems for the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in Monger spaces and we also give a set of alternative conditions in place of completeness of the space. We improve and extend the results of Dedeic & Sarapa ［A common fixed point theorem for three mappings on Monger spaces. Math. Japon. 34 (1989), no. 6,919-923］ and Rashwan & Hedar ［On common fixed point theorems of compatible mappings in Monger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546］.

• East Asian mathematical journal
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• v.27 no.5
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• pp.573-583
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• 2011

In this paper, we prove a common fixed point theorem for noncompatible, discontinuous mappings on a Banach space. Our main theorem extends, improves, generalizes some known results on Banach spaces.