A REVIEW OF FIXED POINT THEORY IN E-FUZZY METRIC SPACES
Volume: 15 - Issue: 09 - Date: 30-09-2026
Approved ISSN: 2278-1412
Published Id: IJAECESTU508 | Page No.: 106-113
Author: Megha Chourasia
Co- Author: Uday Dolas
Abstract:-Fixed point theory supplies a rigorous framework for establishing existence, uniqueness, approximation and stability of solutions of nonlinear equations. Its classical development begins with Banach’s contraction principle and extends through Kannan, Chatterjea, Reich, Zamfirescu, Hardy-Rogers and other generalized contractions. The emergence of fuzzy set theory and fuzzy metric spaces subsequently made it possible to analyze nearness, convergence and iterative behavior when distance information is uncertain or graded rather than crisp. This review critically examines that development and focuses on the relatively recent literature on E-fuzzy metric spaces. Particular attention is given to structural properties, convergence and E-Cauchy sequences, completeness, Banach-type, Kannan-type and Chatterjea-type contractions, common fixed points, compatibility and weak compatibility, stability, well-posedness and nonlinear applications. The review also emphasizes a terminological issue: the expression “E-fuzzy metric space” is not completely uniform in the literature. One important strand associated with Sukanya and Jose develops a generalized, three-variable fuzzy metric structure related to G-metric ideas, whereas Mecheraoui et al. use the same label for a particular class of George-Veeramani fuzzy metric spaces with an additional uniformity property. Accordingly, the axiom system must be fixed explicitly before new theorems are stated. Recent E-fuzzy studies on contraction theorems, coupled fixed points, tripled fixed points and common fixed points indicate that the area remains open for systematic comparison of contractive classes, assumption reduction, stability and well-posedness. The review concludes by mapping these gaps to the objectives and hypotheses of the proposed thesis and by identifying a coherent program for new theorem development and applications.
Key Words:-E-fuzzy metric space; fuzzy metric space; fixed point theorem; Banach contraction; Kannan contraction; Chatterjea contraction; common fixed point; compatibility; weak compatibility; E-Cauchy sequence; completeness; stability; well-posedness; nonlinear analysis.
Area:-Applied Mathematics
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