The notion of symmetry is the main property a metric function. area fixed point theory has suitable structure for in mathematics. goal this paper to find and common results bicomplex valued b-metric space mixed type rational contractions with control functions. Some well-known literature findings were generalized our findings. We provide an example strengthen validate results. As example, conte...

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

In this paper we introduce the notion of an F-metric, as a function valued distance mapping, on a set X and we investigate the theory of F-metric spaces. We show that every metric space may be viewed as an F-metric space and every F-metric space (X, δ) can be regarded as a topological space (X, τδ). In addition, we prove that the category of the so-called extended Fmetric spaces properly contai...

We overview recent results on generalizations of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices and of matrix-valued distributions, as well as some extensions of the theory to vector-valued distributions and discrete spaces (weighted graphs). Dedicated to Professor Mathukumalli Vidyasagar on his 70th birthday.

banach contraction principle has been generalized in different spaces by mathematicians over the years. mustafa and sims [18] proposed a new class of generalized metric spaces, which are called as g-metric spaces. in this type of spaces a non-negative real number is assigned to every triplet of elements. many mathematicians studied extensively various results on g-metric spaces by using the con...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...