The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study modular function spaces. We first introduce concepts ρ-contractions and ρ-Kannan then establish some Banach Contraction Principle type theorems for existence fixed points such setting. Our results are generalizations corresponding from to those contractions ρ-contractions. make ever a...

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...

Recommended by Mohamed Khamsi Let S be a left amenable semigroup, let S {T s : s ∈ S} be a representation of S as Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition, let {μn} be a strongly left regular sequence of means defined on an S-stable subspace of l∞ S , let f be a contraction on C, and let {αn}, {βn}, and...

The purpose of this paper is to introduce a general iterative method for finding solutions of a general system of variational inclusions with Lipschitzian relaxed cocoercive mappings. Strong convergence theorems are established in strictly convex and 2-uniformly smooth Banach spaces. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of strict pse...

Banach initiated the study of fixed points through iterative sequences, which appeared as a base for metric fixed point theory. Many authors continue this pattern of finding fixed points, see for eaxmple [1]-[29]. Samet . al et [1] introduced the ideas of  - -contractive and  -admissible mappings and got fixed points of the mappings through iterative sequence satisfying these ideas on comple...

We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

Introduction/purpose: This article establishes several new contractive conditions in the context of so-called F-metric spaces. The main purpose was to generalize, extend, improve, complement, unify and enrich already published results existing literature. We used only property (F1) Wardowski as well one well-known lemma for proof that Picard sequence is an F-Cauchy framework space. Methods: Fix...

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...

The main purpose of this paper is to improve, generalize, unify, extend and enrich the recent results established by Dung Hang (2015), Piri Kumam (2014, 2016), Singh et al. (2018). In our proofs, we only use property (F1) Wardowski’s F-contraction, while many authors in their papers still all tree properties F-contraction as well two new introduced Kumam. Our approach indicates that for most wi...

In this paper, by using the concept of \(\alpha,\beta\)-admissible mappings with respect to \(Z\)-contraction, we prove some fixed point results in complete metric-like spaces. Our generalize and extend several well-known on literature. An example is given support obtained results.