We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...

Clustering methods are one of the key steps that lead to the transformation of data to knowledge. Clustering algorithms aim at partitioning an initial set of objects into disjoint groups (clusters) such that that objects in the same subset are more similar to each other than objects in different groups. In this paper we present a generalization of the k-Windows clustering algorithm in metric sp...

As a counterpart to best approximation, a new kind of approximation, called best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi. In this paper, we use this coapproximation to prove some results on the existence and uniqueness of best coapproximation in quotient spaces when the underlying spaces are metric linear spaces. We shall also see how coproximinality ...

‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

1 We develop the method of anholonomic frames with associated nonlinear connection (in brief, N–connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton spaces) can be modelled on the metric–affine spaces. There are formulated the criteria when such generalized Finsler metrics are effectively defined in the Einstein, telepa...

let (x, d) be a compact metric space and f : x → x be a continuous map. consider the metric space (k(x),h) of all non empty compact subsets of x endowed with the hausdorff metric induced by d. let ¯ f : k(x) → k(x) be defined by ¯ f(a) = {f(a) : a ∈ a} . we show that block-coppels chaos in f implies block-coppels chaos in ¯ f if f is a bijection.

Abstract. For metric measure spaces verifying the reduced curvature-dimension condition CD∗(K,N) we prove a series of sharp functional inequalities under the additional assumption of essentially nonbranching. Examples of spaces entering this framework are (weighted) Riemannian manifolds satisfying lower Ricci curvature bounds and their measured Gromov Hausdorff limits, Alexandrov spaces satisfy...

In this paper we define weak $F$-contractions on a‎ ‎metric space into itself by extending $F$-contractions‎ ‎introduced by D‎. ‎Wardowski (2012) and provide some fixed point‎ ‎results in complete metric spaces and in partially ordered complete ‎generalized metric spaces‎. ‎Some relationships between weak‎ ‎$F$-contractions and $Fi$-contractions are highlighted‎. ‎We also ‎give some application...