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Abstract  

Using the theory of countable extension of t-norm we prove a common fixed point theorem for compatible mappings satisfying an implicit relation in fuzzy metric spaces.

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Abstract  

In the recent paper [1] the claim is made that a probabilistic version of a common fixed point theorem of Pant holds. We provide some examples to demonstrate that this claim is false unless some additional conditions are imposed. Our note is desired to complete the interesting results in the quoted paper.

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The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [1,2,4–9,11–15].

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Abstract  

In the recent paper of this journal [7], a common fixed point theorem in G-complete fuzzy metric spaces under the t-norm Min was proved. We show that this theorem actually holds in more general situations.

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Abstract  

We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper.

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Acta Mathematica Hungarica
Authors:
Lj. B. Ćirić
,
Lj. B. Ćirić
,
Lj. B. Ćirić
,
N. T. Nikolić
,
N. T. Nikolić
,
N. T. Nikolić
,
Ume J. S.
,
Ume J. S.
, and
Ume J. S.

Summary  

Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ćirić and Rhoades and Watson.

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Abstract  

We prove new common fixed point theorems for weakly compatible mappings on uniform spaces. Also, an application to locally convex spaces is presented.

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Abstract  

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc.

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