In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuz...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

background: the marginal length from main tumor in esophageal cancer is a considerable issue regarding surgical management and adjuvant treatment; so we decided to study the contractility effect on the proximal surgical margin after immersing it in10% buffered formalin as a fixative. methods: the proximal marginal length of  ten sequential patients with esophageal cancer who underwent transhiat...

The proximal point algorithm (PPA) is classical, and the resulting proximal subproblems may be as difficult as the original problem. In this paper, we show that with appropriate choices of proximal parameters, the application of PPA to the linearly constrained convex programming can result in easy proximal subproblems. In particular, under some practical assumptions on the objective function, t...

A subthreshold pharyngeal stimulus induces lower esophageal sphincter (LES) relaxation and inhibits progression of ongoing peristaltic contraction in the esophagus. Recent studies show that longitudinal muscle contraction of the esophagus may play a role in LES relaxation. Our goal was to determine whether a subthreshold pharyngeal stimulus induces contraction of the longitudinal muscle of the ...

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions Geraghty type. Additionally, in 2021, Beg concept generalized F-proximal contraction first kind and second kind, respectively. After developing these concepts, authors mainly studied best proximity points for classes mappings. this short note, we prove that problem existence said proximal is equivalent to ...

In this paper, we introduce some new classes of proximal contraction mappings and establish  best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...