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Abdelkarim Kari

Publications and source records attributed to Abdelkarim Kari.

5 recordsLinked to original sources
arXiv2024

Fixed point theorems for generalized $θ-ϕ-$contraction mappings in rectangular quasi b-metric spaces

A generalized version of both rectangular metric spaces and rectangular quasi-metric spaces is known as rectangular quasi b-metric spaces (RQB-MS). In the current work, we define generalized $( θ,ϕ) $-contraction mappings and study fixed point (FP) results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results generalize many existing results. We also provide examples in support of our main findings.

math.MG↗
arXiv2023

Best proximity point of generalized $θ-ϕ-$proximal non-self contractions

In this manuscript, motivated and inspired by results of Best proximity point of generalized $ F $-proximal non-self contractions, we introduce the concept of generalized $θ-ϕ-$proximal contraction and prove new best proximity results for these contractions in the setting of a metric space. Our results generalize and extend many recent results appearing in the literature. An example is being given to demonstrate the usefulness of our results.

math.FA↗
arXiv2022

New fixed point theorems for $(ϕ, F)-$contraction on rectangular b-metric spaces

The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions. In this paper, inspired by the concept of $(ϕ, F)-$contraction in metric spaces, introduced by Wardowski. We present the notion of $(ϕ, F)-$contraction in $b-$rectangular metric spaces to study the existence and uniqueness of fixed point for the mappings in this spaces. Our results improve many existing results.

math.GN↗
arXiv2022

Fixed point theorems in controlled rectangular metric spaces

In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality as follows: \begin{equation*} d(x, y)\leqα(x, u)d(x, u)+α(u, v)d(u, v)+α(v, y)d(v, y), \end{equation*} for all distinct $x, y, u, v\in X$ with the function $α: X\times X\rightarrow[1,\infty[$. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.

math.GN↗