Some new theorems for cyclic contractions in Gb-metric spaces and some applications

Min Liang, Chuanxi Zhu, Chunfang Chen and Zhaoqi Wu

Applied Mathematics and Computation, 2019, vol. 346, issue C, 545-558

Abstract: In this paper, some new theorems for various cyclic contractions are established in Gb-metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations, which generalize many known results in corresponding literatures. On the other hand, we introduce the notion of the cyclic α-ψφ-contractive mappings in Gb-metric spaces and establish a new fixed point theorem, which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations. Moreover, some examples are given to support our main results.

Keywords: Gb-metric space; Cyclic α-ψφ-contraction; Fixed point; Integral equation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:545-558

DOI: 10.1016/j.amc.2018.10.028

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