Pata-Type Fixed-Point Theorems in Kaleva–Seikkala’s Type Fuzzy Metric Space

<abstract><p>Among various improvements in fuzzy set theory, a progressive development has been in process to investigate fuzzy analogues of fixed point theorems of the classical fixed point results. In this direction, taking the ideas of $ \theta $-contractions as well as Feng-Liu's approach into account, some new fuzzy fixed point results for nonlinear fuzzy set-valued $ \theta $-contractions in the framework of metric-like spaces are introduced in this paper without using the usual Pompeiu-Hausorff distance function. Our established concepts complement, unify and generalize a few important fuzzy and classical fixed point theorems in the corresponding literature. A handful of these special cases of our notions are pointed and analyzed. Some of the main results herein are further applied to derive their analogues in metric-like spaces endowed with partial ordering and binary relations. Comparisons and nontrivial examples are given to authenticate the hypotheses and significance of the obtained ideas.</p></abstract>

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Pata-Type Fixed-Point Theorems in Kaleva–Seikkala’s Type Fuzzy Metric Space

Abstract: The purpose of this paper is to generalize the fixed-point theorems for Banach–Pata-type contraction and Kannan–Pata-type contraction from metric spaces to Kaleva–Seikkala’s type fuzzy metric spaces. Moreover, two examples are given for the support of our results.

Cited by 2 publications

References 15 publications

On fuzzy inner products constructed by fuzzy numbers in linear spaces

On fuzzy inner products constructed by fuzzy numbers in linear spaces

On nonlinear fuzzy set-valued $ \Theta $-contractions with applications

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