Abstract
The purpose of this paper is to emphasize the role of âcommon limit range propertyâ to ascertain the existence of common fixed points in modified intuitionistic fuzzy metric spaces enjoying an implicit function utilized in Tanveer et al. (2012) and Imdad et al. (2012). As an application to our main result, we derive a fixed point theorem for finite families of self-mappings. We also give some examples which demonstrate the validity of the hypotheses and degree of generality of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature.
Highlights
The fruitful and productive idea of fuzzy set was initiated by Zadeh [1]
We extend common limit range property for two pairs of self-mappings in the framework of modified IFMS (X, MM,N, T) as follows
We indicate that Theorem 48 can be utilized to derive common fixed point theorems for any finite number of mappings
Summary
The fruitful and productive idea of fuzzy set was initiated by Zadeh [1]. In an attempt to generalize the idea of fuzzy set, Atanassov [2] introduced the notion of intuitionistic fuzzy set. Chauhan et al [28, 29] and Sintunavarat et al [14] proved some interesting fixed point results for mappings defined on modified IFMS via common limit range property. Imdad et al [30] extended the notion of common limit range property to two pairs of self-mappings and proved some fixed point results in Menger and metric spaces. In this paper, utilizing an implicit function due to Tanveer et al [22] ( Imdad et al [23]), we prove some common fixed point theorems for two pairs of weakly compatible mappings in modified IFMS employing the common limit range property. Some related results are derived besides furnishing illustrative examples
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