A Note on the Fixed Point of Generalized Eventual Cyclic Gross Contractive Mappings

Abstract

Based on the work of Agarwal et al., in press, we introduce a concept of generalized eventual cyclic gross contractive mapping in metric spaces, which is a generalization of the eventual cyclic gross contractions. Furthermore, we analyze the existence of a fixed point for this type of contractive mapping, and present a new and general fixed point theorem.

Fixed Point of Generalized Eventual Cyclic Gross in Fuzzy Norm Spaces for Contractive Mappings

“…If l > 0, Then we have λ ≥ 1 2 , which is a contradiction. Furthermore, λ = 1 2 is also impossible by [4]. So,…”

“…Therefore, {T n u} is a Cauchy sequence. For λ = 1 2 , by [4], we know that {T n u} also is a Cauchy sequence. Therefore,…”

“…In this paper, starting from the article of Jin Liang and Sheng-Hua Yan [4], we study generalized eventual cyclic gross contractive mapping on fuzzy norm spaces, and we give some fuzzy fixed points of such mapping. Fuzzy set was defined by Zadeh [12].…”