Fixed Points and Cyclic Contraction Mappings Under Implicit Relations and Applications to Integral Equations - Nashine, Hemant Kumar (Sarajevo Journal of Mathematics, 2024)
Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is originated. As a result, we derive existence and uniqueness results of fixed points for such mappings. We furnish suitable examples to demonstrate the validity of the hypotheses of our results. The results will be applied to the study of the existence and uniqueness of solutions for a class of nonlinear integral equations. 2010 Mathematics Subject Classification. Primary: 54H25; Secondary: 47H10.