Well-Posedness and Ulam's Stability of Functional Equations in $\mathcal{F}$-metric space with an application

Abstract

In this paper, we consider a fixed point problem related to some contraction mappings and give a new class of Picard operators for such class of mappings in a framework of $\mathcal{F}$-metric space and obtain some interesting and new results. As application of the obtain results, we investigate the Hyers-Ulam stability of fixed point problem, Cauchy functional equation and integral equation. Also, we present the well-posedness of fixed point problem and integral equation. Some illustrative examples are also provided to support the new findings.