• East Asian mathematical journal
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• 제18권2호
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• pp.183-193
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• 2002

The aim of this paper is to prove a common fixed point theorem from the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in fuzzy 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.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.395-405
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• 2011

In this paper, we prove a common fixed point theorem for a pair of weakly compatible maps under E.A. property.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.271-287
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• 2022

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d^*) satisfying the following ξ-weakly expansive condition: d^*(𝒫c, 𝒫d) ≥ d^* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.729-740
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• 2012

In this paper, we prove common fixed point theorems for occasionally weakly compatible maps in Menger spaces with a continuous t-norm of H-type. As application to our results, we obtain the corresponding fixed point theorems in metric spaces. Our results improve and generalize many known results in Menger spaces as well as in metric spaces.

• 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.

• East Asian mathematical journal
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• 제27권5호
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• pp.565-572
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• 2011

In this paper we prove common fixed point of weakly compatible maps without continuity in Menger spaces. We show that continuity of any mapping is not required for the existence of fixed point. We improve some earlier results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권2호
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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］.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.155-164
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• 2013

In this paper, we have established some common fixed point theorems for two pairs of occasionally weakly compatible hybrid maps sat-isfying a strict contractive condition in a non-archimedean fuzzy metric space. Our result extend, generalized and fuzzify several fixed point theo-rems on metric space.