In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality d(x, y) ≤ σ(d(x, z) +d(z, y)) for some constant σ ≥ 1, rather than the usual triangle inequality. Such a space is called a nearmetric space. We show that many well-known results in metric spaces (e.g. Ascoli-Arzelà theorem) still hold in nearmetric...

We unify the concepts of G-metric, metric-like, and b-metric to define new notion of generalized b-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes of G-α -admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, so...

In this paper, we consider a new random iteration process to approximate a common random fixed point of a finite family of uniformly quasi-Lipschitzian random mappings in generalized convex metric spaces. Our results presented in this paper extend and improve several recent results. c ©2016 All rights reserved.

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality d(x, y) ≤ σ(d(x, z) +d(z, y)) for some constant σ ≥ 1, rather than the usual triangle inequality. Such a space is called a quasimetric space. We show that many well-known results in metric spaces (e.g. Ascoli-Arzelà theorem) still hold in quasimetr...

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.

We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle, Ćirić’s fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces recover various topological spaces including standard metric spac...

Generalized Extreme Learning Machine (GELM) is a kind of fast and efficient learning algorithm for training Generalized Single-layer hidden Feedforward Networks (GSLFNs) acting on some metric spaces. However, noisy data often produce over-fitting phenomena in practical applications. Therefore, an improved learning algorithm, called Regularized Generalized Extreme Learning Machine (R-GELM), is p...

The aim of this paper is to establish fixed-point theorems for generalized M -fuzzy 2-metric space. Our theorem in an extension of result of Fisher [6], Sharma [19], Sharma, Sharma and Iseki [20], Sedghi and Shobe [22] and Veerapandi, et. al.[28]. Mathematics Subject Classification: 47H10, 54H25

The notion of gradient flows is generalized to a metric space setting without any linear structure. The metric spaces considered are a generalization of Hilbert spaces, and the properties of such metric spaces are used to set up a finite-difference scheme of variational form. The proof of the Crandall–Liggett generation theorem is adapted to show convergence. The resulting flow generates a stro...