Fixed Point Results in tvs-Cone b-Metric Spaces with Applications to Fredholm Integral Equations

The aim of this research article is to explore the framework of tvs-cone b-metric spaces and establish some generalized common fixed point theorems for self mappings under generalized contractive conditions. To extend this theory, we introduce the notion of a generalized Hausdorff distance function in the framework of tvs-cone b-metric spaces and prove some novel fixed point results for multi-valued mappings. Our findings naturally encompass and generalize several known results in tvs-cone metric spaces, cone b-metric spaces, and cone metric spaces. To illustrate the applicability of the developed framework, we apply the main results to Fredholm integral equations.