Generalized fuzzy GV-Hausdorff distance in GFGV-fractal spaces with application in integral equation

Abstract

We propose a method for constructing a generalized fuzzy Hausdorff distance on the set of the nonempty compact subsets of a given generalized fuzzy metric space in the sence of George–Veeramni and Tian–Ha–Tian. Next, we define the generalized fuzzy fractal spaces. Morever, we obtain a fixed point theorem of a class of generalized fuzzy contractions and present an application in integranl equation.

The Hausdorff–Pompeiu Distance in Gn-Menger Fractal Spaces

“…For more details about Gn-Menger space and distance, see [5][6][7][8][9][10][11][12][13][14][15]. Our results improve and generalize recent results in [16][17][18].…”

A Study on Hutchinson-Barnsley Theory in Product Intuitionistic Fuzzy Fractal Space

“…Uthayakumar [21] on complete and compact spaces. This elucidative note reveals the HB theory in intuitionistic fuzzy metric space and its properties.…”

“…Definition 3.1 [21] Suppose that is an intuitionistic fuzzy metric space and are N-intuitionistic fuzzy B-contractions (respectively N-intuitionistic fuzzy Edelstein contractions) with the corresponding contractivity ratios . Then the collection is designated as an intuitionistic fuzzy iterated function system in the intuitionistic fuzzy metric space .…”

“…Theorem 3.2 [21] Assume is an intuitionistic fuzzy metric space. Let be the Hausdorff intuitionistic fuzzy metric space relative to the intuitionistic fuzzy metric space.…”

“…Further, an analysis of the fuzzy fractal space and intuitionistic fuzzy fractal space was done by Easwaramoorthy and Uthayakumar [20,21] . In their work, they investigated the attractors constructed by the iterated function system of fuzzy contractive functions in both fuzzy metric space and intuitionistic fuzzy metric space by generalizing the HB theory.…”