We define discrete Menger-type curvature of d+2 points in a real separable Hilbert space H by an appropriate scaling of the squared volume of the corresponding (d+1)-simplex. We then form a continuous curvature of an Ahlfors regular measure μ on H by integrating the discrete curvature according to products of μ (or its restriction to balls). The essence of this work, which continues in a subseq...

In this paper we prove a fixed point theorem for six mappings in Menger space using the notion of weakly compatible.

The main purpose of this paper is to prove a common fixed point theorem for two pairs of weakly compatible mappings in Menger space using implicit relation.

Probabilistic metric space was first introduced by Menger [6]. Later, there are many authors who have some detailed discussions and applications of a probabilistic metric space, for example, we may see Schweizer and Sklar [8]. Besides, there are many results about fixed point theorems in a probabilistic metric space with contractive types having appeared; we may see the papers [1–3, 9–12]. In t...

Most mathematical theories start from humble beginnings where a mathematician while examining some mathematical object makes fundamental, but ad hoc, observations. When the significance of these observations are realized some organised study begins during which these are explored in detail for some central examples. In this second part of theory building some general themes of investigation are...

In this work, we introduce the notions of Star-?K and absolutely spaces which allow us to unify results among several properties in theory star selection principles on small spaces. particular, selective versions Menger, Hurewicz Rothberger property (a) regarding size space. Connections other well-known are mentioned. Furthermore, absolute version neighbourhood principle introduced. As an appli...

In this paper we primarily introduce the local version of star-Menger property, namely locally property (a space with is called star-Menger) and present some important topological observations. Certain interactions between new notion are also observed. Some observations on effectively Pixley-Roy hyperspaces (introduced here) obtained. Preservation like properties under several operations interp...

Menger called a finitely-compact metric space in which any two distinct points are contained in exactly one set congruent to a euclidean straight line a straight-line space (S.L. space) [ l ] . 1 He observed that in such spaces a segment (or vector) addition can be defined in a very simple way (see §2 of the present paper) which satisfies all requirements for an abelian group except, in general...