On modified α-ϕ-fuzzy contractive mappings and an application to integral equations

Abstract

We introduce the notion of a modified α-φ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory. MSC: 47H10; 45D05

Some fuzzy common fixed point theorems using common limit in the range property with an application

“…Here, we study the existence and uniqueness of the solution of a Volterra integral equations of the second kind, using our results. Inspired by [12], we consider the integral equation 1x(r) = g(r) + x ∈ X, and the induced metric…”

“…A class of mathematicians are working in this area and trying to obtain solutions of the integral equations using their results. Recently, Mishra et al [12] introduce the notion of a modified α-φ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. As an application, they study the existence and uniqueness of the solution to integral equation.…”

“…As an application, they study the existence and uniqueness of the solution to integral equation. Some applications of fixed point theorems in metric or fuzzy metric theory can be seen in [2,3,4,7,9,11,12,16,17,18,25].…”

Fixed Point Results via α-Admissibility in Extended Fuzzy Rectangular b-Metric Spaces with Applications to Integral Equations

“…Stimulated by this work, Gopal and Vetro [18] introduced the concept of α-φ-contractive mapping and established some theorems for G-complete fuzzy metric spaces in the sense of Grabiec [6]. Later, many researchers explored α-admissibility in fuzzy metric spaces (see [18,23,24]). We also mention the recent extension to spaces endowed with a graph given in [25].…”

A short and sharpened way to approach fixed point results involving fuzzy $\mathcal{H}$-contractive mappings

“…Later, Beg et al [11] defined the notion of α-fuzzy-H-contractive mapping and established some existence and uniqueness of fixed point results in fuzzy M-complete metric spaces. For more results in this direction, we refer the reader to [12][13][14][15][16][17][18][19][20][21][22][23][24].…”