On the solutions of a class of nonlinear integral equations in cone $b$-metric spaces over Banach algebras

Authors

  • L.T. Quan Department of Mathematics, Vinh University, Vinh City, Nghe An Province, Vietnam
  • T. Van An Department of Mathematics, Vinh University, Vinh City, Nghe An Province, Vietnam
https://doi.org/10.15330/cmp.11.1.163-178

Keywords:

cone $b$-metric space over Banach algebra, $\varphi$-contraction, ${\bf c}$-sequence, fixed point, integral equation
Published online: 2019-06-30

Abstract

In this paper, we study the existence of the solutions of a class of functional integral equations by using some fixed point results in cone $b$-metric spaces over Banach algebras. In order to obtain these results we introduced and proved some properties of generalized weak $\varphi$-contractions, in which the $\varphi$ are nonlinear weak comparison functions. The obtained results are generalizations of results of Van Dung N., Le Hang V. T., Huang H., Radenovic S. and  Deng G. Also, some suitable examples are given to illustrate obtained results.

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How to Cite
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Quan, L.; Van An, T. On the Solutions of a Class of Nonlinear Integral Equations in Cone $b$-Metric Spaces over Banach Algebras. Carpathian Math. Publ. 2019, 11, 163-178.