Remarks on the generalized interpolative contractions and some fixed-point theorems with application

Abstract

In this manuscript, some remarks on the papers [H. A. Hammad, P. Agarwal, S. Momani, and F. Alsharari, Solving a fractional-order differential equation using rational symmetric contraction mappings, Fractal Fract. 5 (2021), 159] and [A. Hussain, F. Jarad, and E. Karapinar, A study of symmetric contractions with an application to generalized fractional differential equations, Adv. Differ. Equ. 2021 (2021), 300] are given. In the light of remarks, we introduce a new property that makes it convenient to investigate the existence of fixed points of the interpolative contractions in the orthogonal metric spaces. We derive several new results based on known contractions from the main theorems. As an application, we resolve a Urysohn integral equation.

Fractional Differential Boundary Value Equation Utilizing the Convex Interpolation for Symmetry of Variables

“…Hussain [8][9][10] recently expanded this idea of Karapinar and published a few findings pertaining to these kinds of novel contractions. Nazam et al [11][12][13] introduced (Ψ, Φ)-orthogonal interpolative contractions very recently and made a few observations in the literature.…”