Interpolative fuzzy Z-contraction with its application to Fredholm non-linear integral equation

Shobha Jain, S. Radenović
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引用次数: 0

Abstract

The aim of this paper is to introduce the notion of interpolative fuzzy Z-contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the existing fuzzy contractions (by Gregori and Sapena [6]), ψ contraction (by Mihet [11]), fuzzy Z-contractions (by Shukla et al. [21]) and Tirado contraction (by Tirado [22]), which are for only one self map. Using this, we establish a unique common fixed point theorem for two self maps satisfying condition (S), which was introduced by Shukla et al. in [21] through weak compatibility. As an applications, we discuss fixed point theorem for Fredholm non-linear integral equation. The article also includes an example, which shows the validity of our results.
插值模糊z压缩及其在Fredholm非线性积分方程中的应用
本文的目的是引入模糊度量空间中对自映射的插值模糊z -压缩条件的概念,它扩大、统一和推广了已有的只针对一个自映射的模糊压缩(Gregori和Sapena[6])、ψ压缩(Mihet[11])、模糊z -压缩(Shukla et al.[21])和Tirado压缩(Tirado[22])。利用这一点,我们建立了Shukla等人在[21]中通过弱相容引入的满足条件(S)的两个自映射的唯一公共不动点定理。作为应用,讨论了Fredholm非线性积分方程的不动点定理。文中还给出了一个算例,说明了我们的结果的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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