Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces

Abstract

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. Using these results, we prove theorems for various types of well-known generalized contractions in fuzzy normed spaces. Also, we apply our results to get an application of approximate fixed point and approximate best proximity pair theorem of their diameter.

Keywords

• Cyclic maps
• $alpha$-asymptotically regular
• $F$-Kannan operator
• Fuzzy diameter