The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. Next, we obtain cone $b$-metric version of these results by using a scalarization function. Our results extend and generalize several well known comparable results in the existing literature.

For a given metric space (S, d), let us use the term “standard σ-field” to denote the σ-field S of subsets of S generated by the open balls (in the metric d). A function f : S×S×S× . . .→ S is “measurable” (with respect to S) if for every set A ∈ S one has that f−1(A) is a member of S×S×S×. . . , the product σ-field on S × S × S × . . . . Suppose B is a separable real Banach space. Suppose (Ω,F...

In this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On xed-point the- orems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252].

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

We consider maximum b-matching problems where the nodes of the graph represent points in a metric space, and the weight of an edge is the distance between the respective pair of points. We show that if the space is either the rectilinear plane, or the metric space induced by a tree network, then the b-matching problem is the dual of the (single) median location problem with respect to the given...

Let (DS, QS, sim) be a retrieval system consisting of a document space DS, a query space QS, and a function sim, expressing the similarity between a document and a query. Following Everett and Cater, we introduce topologies on the document space. These topologies are generated by the similarity function sim and the query space QS. Three topolgies will be studied : the retrieval topology, the si...

The current study attempts to identify a new generalized metric space structure, referred as partial modular b−metric, that extends both via b−metric and explains the topological aspects of implementing examples. In addition, contraction mapping modified interpolative almost E−type is determined, which an interpretation bestowed with E−contraction well simulation function fixed point theorem en...

‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...

1.1. Normed spaces. Recall that a (real) vector space V is called a normed space if there exists a function ‖ · ‖ : V → R such that (1) ‖f‖ ≥ 0 for all f ∈ V and ‖f‖ = 0 if and only if f = 0. (2) ‖af‖ = |a| ‖f‖ for all f ∈ V and all scalars a. (3) (Triangle inequality) ‖f + g‖ ≤ ‖f ||+ ‖g‖ for all f, g ∈ V . If V is a normed space, then d(f, g) = ‖f−g‖ defines a metric on V . Convergence w.r.t ...