Solvability of Integral Equations through Fixed Point Theorems

Abstract

The thesis content primarily belongs to the domain of Integral Equations interacting newline with Functional Analysis under Mathematics Subject Classification No. 47H10; 54H25; newline 34A08; and 15A24. The primary focus of the investigation pertains to the behavior of newline mappings on different space structure. newline The thesis studies the presence of fixed point findings in solving integral equations newline within the context of extended Branciari b-metric spaces, and#945;and#8722; complete extended Bran newlineciari b-metric spaces and relational metric spaces (not necessarily partial order) with newline w-distance. In order to do this, firstly a FG-contractive conditions in extended Bran newlineciari b- distance spaces is introduced and derived fixed points results for triangular newline and#945;-admissible mappings, followed by some suitable examples. Secondly, a notion of an newline and#945;-complete extended Branciari b-distance space and rational and#945; and#8722; and#946; and#8722; JS-contractive newline conditions are introduced, and derived coincidence points, common fixed points, and newline uniqueness of fixed points for two pairs of mappings in underlying space. Then these newline f newline indings were used to find a solution to the system of Urysohn Integral equations . Fi newlinenally, a p-implicit R- contractive mappings in a relational metric spaces (not necessarily newline partial order) with w-distance is introduced, and established new fixed point results, and newline justified these notions and results with relevant examples. Further, the outcomes are ap newlineplied to establish sufficient criteria in order for fractional differential equation solutions newline to exist that lead to integral equations. The established fixed point result is also used to newline solve nonlinear matrix equations. Convergence analysis is carried out with respect to newline various initializations with geometrical demonstration. newline Keywords: , Fixed Point, Integral Equations, and#945;-Admissible Mappings, Extended Branciari b-distance spaces, w-distance Function, Implicit Relation, Nonlinear Matrix Equation, Fractional differential Equation, Urysohn Integral Equations newline