Extensions of Orthogonal p-Contraction on Orthogonal Metric Spaces

Fixed-point theory and symmetry are major and vigorous tools to working nonlinear analysis and applications, specially nonlinear operator theory and applications. The subject of examining the presence and inimitableness of fixed points of self-mappings defined on orthogonal metric spaces has become very popular in the latest decade. As a result, many researchers reached more relevant conclusions. In this study, the notion of phi-Kannan orthogonal p-contractive conditions in orthogonal complete metric spaces is presented. W-distance mappings do not need to satisfy the symmetry condition, that is, such mappings can be symmetrical or asymmetrical. Self-distance does not need to be zero in w-distance mappings. The intent of this study is to enhance the recent development of fixed-point theory in orthogonal metric spaces and related nonlinear problems by using w-distance. On this basis, some fixed-point results are debated. Some explanatory examples are shown that indicate the currency of the hypotheses and grade of benefit of the suggested conclusions. Lastly, sufficient cases for the presence of a solution to nonlinear Fredholm integral equations are investigated through the main results in this study.