Solution of Nonlinear Integral Equation via Fixed Point of Cyclic $$\alpha _{L}^{ \psi }$$αLψ-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.