$\alpha_\kappa-$Implicit Contraction in non-AMMS with Some Applications

Abstract

In this article, we establish $\alpha_\kappa-$implicit contraction and provide some fixed point results in non-AMMS. Our results progress and generalize some famous consequences in a suitable resource. As an implementation, we study stability in the sense of Ulam-Hyers and a fixed point problem's well-posedness. In addition, some examples are given for new concepts. Also, an application to integral equations is discussed.