Solution of Nonlinear Integral Equation via Fixed Point of Cyclic \(\alpha _{L}^{ \psi }\)-Rational Contraction Mappings in Metric-Like Spaces

Abstract

In this paper, we introduce the notions of \(\alpha _{L}^{\psi }\)-rational contractive and cyclic \(\alpha _{L}^{\psi }\)- rational contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric-like spaces (dislocated metric spaces). The results presented here substantially generalize and extend several comparable results in the existing literature. As an application, we prove new fixed point results for \(\psi L\)-graphic and cyclic \(\psi L\)-graphic rational contractive mappings. Moreover, some examples and an application to integral equation are presented here to illustrate the usability of the obtained results.

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Correspondence to Manuel De la Sen.

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Hammad, H.A., De la Sen, M. Solution of Nonlinear Integral Equation via Fixed Point of Cyclic \(\alpha _{L}^{ \psi }\)-Rational Contraction Mappings in Metric-Like Spaces. Bull Braz Math Soc, New Series 51, 81–105 (2020). https://doi.org/10.1007/s00574-019-00144-1

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Keywords

  • Cyclic contractive mapping
  • \(\alpha \)-Admissible
  • Nonlinear integral equations

Mathematics Subject Classification

  • 46N40
  • 47H10
  • 46T99