Approximate Fixed Point Theorems in Fuzzy Norm Spaces for an Operator

Abstract

We define approximate fixed point and fuzzy diameter in fuzzy norm spaces. We prove theorems for various types of well-known generalized contractions on fuzzy norm spaces with the use of two general lemmas that are given regarding approximate fixed points of operators on fuzzy norm spaces.

Approximate Best Proximity Pairs in Fuzzy Normed Spaces for Contraction Maps

“…Definition 2.2. [13] Let (U, N ) be a fuzzy normed space, T : U → U, ϵ > 0 and u0 ∈ U. Then u0 is a F z ϵ -approximate fixed point (fuzzy approximate fixed point) of T if for some α ∈ (0, 1)…”

“…Remark 2.1. [13] In this paper we will denote the set of all F z ϵ -approximate fixed points (fuzzy approximate fixed points) of T , for a given ϵ > 0, by…”

“…Definition 2.3. [13] Let T : U → U. Then T has the fuzzy approximate fixed point property (f.a.f.p.p.)…”

“…Chitra and Mordeson [7] introduced the definition of fuzzy norm and thereafter the concept of fuzzy normed space has been introduced and generalized in different ways by Bag and Samanta in [8], [9], [10]. In 2011, Mohsenalhosseini et al [11], introduced the approximate fixed point in fuzzy normed spaces.…”

Three‐Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set

“…Extensive use of fuzzy theory in many different fields has facilitated active research on operators between fuzzy sets [18][19][20]. Operators of various concepts have been defined and studied, but Zadeh's operator concept is commonly studied and utilized.…”