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The aim of this paper is to generalize the results on expansive mappings of Yesilkaya and Aydin from \cite{Yesilkaya}. We give some fixed point results for q-expansive mappings in metric spaces and prove some fixed point theorems for this…
Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…
In a series of papers in the 1960's, S. G\"ahler defined and investigated so-called m-metric spaces and their topological properties. An m-metric assigns to any tuple of m+1 elements a real value (more generally an element in a partially…
In this paper, we introduce the $\mathcal{F}$-metric space concept, which generalizes the metric space notion. We define a natural topology $\tau_{\mathcal{F}}$ in such spaces and we study their topological properties. Moreover, we…
The concept of a $ C $*-algebra-valued metric space was introduced in 2014. It is a generalization of a metric space by replacing the set of real numbers by a $ C $*-algebra. In this paper, we show that $ C $*-algebra-valued metric spaces…
Based on the concept and properties of $C^{*}$-algebras, the paper introduces a concept of $C_{*}$-class functions. Then by using these functions in $C^{*}$-algebra- valued modular metric spaces of moeini et al. [14], some common fixed…
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
In many applications, one deals with nonsmooth functions, e.g., in nonsmooth dynamical systems, nonsmooth mechanics, or nonsmooth optimization. In order to establish theoretical results, it is often beneficial to regularize the nonsmooth…
The Ran-Reurings fixed point theorem [Proc. Amer. Math. Soc., 132 (2004), 1435-1443] is but a particular case of Maia's [Rend. Sem. Mat. Univ. Padova, 40 (1968), 139-143]. A "functional" version of this last result is then provided, in a…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…
Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space…
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…
The fixed point results for generalized Pre\v{s}i\'c type mappings in the setup of $b$-metric spaces are obtained. The stability of fixed point set of Pre\v{s}i\'c type mappings is also established. Several examples are also presented to…
In this article, we introduce the LR-$(\delta,\phi)$ quasi partial $b$-metric space. Also, the common fixed point theorem on complete LR-$(\delta,\phi)$ quasi partial $b$-metric space has been proved. A non-trivial example is also given.
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The major motives of this paper are to study different types of contractive mappings and also to answer an open question of Garai et al. [The contractive principle for mappings in $b_v(s)$-metric spaces, arXiv:1802.03136]. We first set up…
The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…
In this paper, we introduce the concept of partial extended b-metric spaces (PEBMS) as a unification and generalization of extended b-metric spaces and partial b-metric spaces. This new structure incorporates a point-dependent control…
In this paper, a metric on $S_b$-metric space analogous to the Hausdorff metric has been introduced and some basic properties are obtained on multi-valued $S_b$-metric space. Further, the fundamental multi-valued contraction of Nadler(1962)…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…