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

Author

Listed:
  • Liang, Min
  • Zhu, Chuanxi
  • Chen, Chunfang
  • Wu, Zhaoqi

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.

Suggested Citation

  • Liang, Min & Zhu, Chuanxi & Chen, Chunfang & Wu, Zhaoqi, 2019. "Some new theorems for cyclic contractions in Gb-metric spaces and some applications," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 545-558.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:545-558
    DOI: 10.1016/j.amc.2018.10.028
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    References listed on IDEAS

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    1. Radenović, Stojan & Došenović, Tatjana & Lampert, Tatjana Aleksić & Golubovíć, Zorana, 2016. "A note on some recent fixed point results for cyclic contractions in b-metric spaces and an application to integral equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 155-164.
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