Let S : A→ B and T : A→ B be given non-self mappings, where A and B are non-empty subsets of a metric space. As S and T are non-self mappings, the equations Sx = x and T x = x do not necessarily have a common solution, called a common fixed point of the mappings S and T . Therefore, in such cases of nonexistence of a common solution, it is attempted to find an element x that is closest to both ...

Abstract In this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ ( ? , ? ? ? ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpo...

Here the notion of ?-H?-contraction has been proposed to construct some fixed point results single-valued and multivalued mappings in Menger PM spaces. In addition, an existence result integral equation is concerned justify obtained results.

We introduce the concept of generalized \(\beta\) - \(\gamma\) Z contraction mapping with respect to a simulation function ξ and study existence fixed points for such mappings in complete -metric spaces. Further, we extend it partially ordered

The current study attempts to identify a new generalized metric space structure, referred as partial modular b−metric, that extends both via b−metric and explains the topological aspects of implementing examples. In addition, contraction mapping modified interpolative almost E−type is determined, which an interpretation bestowed with E−contraction well simulation function fixed point theorem en...

This work is devoted to presenting a new four-step iterative scheme for approximating fixed points under almost contraction mappings and Reich–Suzuki-type nonexpansive (RSTN mappings, short). Additionally, we demonstrate that the proposed algorithm converges faster than variety of other current schemes. Furthermore, scheme’s ?2—stability result established corroborating example given clarify co...

In this paper, we present a new extension of Banach-Caristi type theorem for multivalued mappings. We show that our result is not consequence version Banach contraction principle due to Nadler. provide an application the solution functional equations.

In this paper, we introduce a new concept of KW-type ?-contraction mixed multivalued mapping. After that, obtain some fixed point results for both and single valued mappings Finally, provide noteworth example to show the effectiveness our result.

In this study, we introduce a new notion, so-called KW-type F-contraction mapping, inspired by the ideas of Wardowski and Klim–Wardowski. Then, investigate existence best proximity point for such mappings considering family, which is larger than family functions that often used in fixed-point results multivalued mappings. To demonstrate effectiveness our result, also give comparative example to...