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

  • Hasanen Abuelmagd Hammad
  • Manuel De la SenEmail author


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.


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

Mathematics Subject Classification

46N40 47H10 46T99 



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Copyright information

© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceSohag UniversitySohagEgypt
  2. 2.Institute of Research and Development of ProcessesUniversity of the Basque CountryLeioaSpain

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