Stability of Some Functional Equations using Fixed Point Approach - Sharma, Ravinder Kumar (My University, 2023)
The thesis has been split into seven chapters, the first of which includes an introduction to the subject matter and a review of the literature, followed by a summary of the thesis's contents. In the second chapter, we obtain a few sufficient conditions for the existence of fixed point in the framework of $\mathcal{F}$-metric space, orthogonal $\mathcal{F}$-metric space, orthogonal metric space, and complete quasi-2-normed space. In the third chapter, we investigate the Hyers Ulam stability of fixed point and Cauchy functional equations in the context of $\mathcal{F}$-metric space. We study properties, equivalence results, and Ulam-type stability for different forms of quadratic functional equations in the fourth chapter. In the fifth chapter, we study the stability of a quartic functional equation in non-Archmedean $\beta$-normed space and complete $(\beta, p)$-normed space. We study the hyperstability of a general linear functional equation in a complete quasi-2-normed space in the sixth chapter. In the last chapter, we study the stability of integral equations in the setting $\mathcal{F}$-metric space and provide a solution for a Caputo-type nonlinear fractional integro-differential equation in the framework of orthogonal metric space.
Keywords: Stability; Quasi-Normed Space; Fixed Point Methods; $(\beta, p)$-Normed Space; Non-Archimedean $\beta$-Normed Space; Quasi-2-Normed Space