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In this article, two types of contractive conditions are introduced, namely extended integral Ϝ -contraction and (ϰ , Ω - Ϝ) -contraction. For the case of two mappings and their coincidence point theorems, a variant of (ϰ , Ω - Ϝ) -contraction has been introduced, which is called (ϰ , Γ 1 , 2 , Ω - Ϝ) -contraction. In the end, the applications of an extended integral Ϝ -contraction and (ϰ , Ω - Ϝ) -contraction are given by providing an existence result in the solution of a fractional order multi-point boundary value problem involving the Riemann–Liouville fractional derivative. An interesting existence result for the solution of the nonlinear Fredholm integral equation of the second kind using the (ϰ , Γ 1 , 2 , Ω - Ϝ) -contraction has been proven. Herein, an example is established that explains how the Picard–Jungck sequence converges to the solution of the nonlinear integral equation. Examples are given for almost all the main results and some graphs are plotted where required. [ABSTRACT FROM AUTHOR]

In this manuscript, the concept of ϝ-contraction is applied to extend the notion of Jaggi-Suzuki-type hybrid contraction in the framework of G-metric space, which is termed Jaggi-Suzukitype hybrid ϝ-(G-α-φ)-contraction, and invariant point results which cannot be inferred from their cognate ones in metric space are established. The results obtained herein provide a new direction and are generalizations of several well-known results in fixed point theory. An illustrative, comparative example is constructed to give credence to the results obtained. Furthermore, sufficient conditions for the existence and uniqueness of solutions of certain nonlinear polynomial and integral equations are established. For the purpose of future research, an open problem is highlighted regarding discretized population balance model whose solution may be investigated from the techniques proposed herein. [ABSTRACT FROM AUTHOR]

This paper presents a novel concept of G -Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones. [ABSTRACT FROM AUTHOR]

In this note, by using basic properties of the recently introduced concepts of generalized metric spaces, new conditions for the existence of a fixed point for weakly type contractive operator which sends a closed subset into the ambient space under consideration are examined. Our obtained result extends and unifies its corresponding ideas in metric and modular spaces. A comparative nontrivial example is provided to show the novelty and preeminence of our proposed notion. [ABSTRACT FROM AUTHOR]