We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results, we obtain general...

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach ...

A Smarandache multi-space is a union of n spaces A1, A2, · · · , An with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric spaces is introduced. Some characteristics of multimetric spaces are obtained and the Banach’s fixed-point theorem is generalized in this paper.

In this paper we present fixed point results for generalized α-ψ-contractive type mappings in dislocated metric spaces. We also provide some examples to illustrate our results. References 1. Banach S., “Surles operations dans les ensembles abstraites et leurs applications”, Fund. Math., 3 (1922), 133-187. 2. Kannan R., “Some results on fixed points”, Bull. Cal. Math. Soc., 60 (1968), 71-76. 3. ...

The properties of the metric topology on infinite and finite sets are analyzed. We answer whether finite metric spaces hold interest in algebraic topology, and how this result is generalized to pseudometric spaces through the Kolmogorov quotient. Embedding into Lebesgue spaces is analyzed, with special attention for Hilbert spaces, `p, and EN .

We introduce a new, simple metric method of sampling metric measure spaces, based on a well-known “snowflakeing operator” and we show that, as a consequence of a classical result of Assouad, the sampling of doubling metric spaces is bilipschitz equivalent to that of subsets of some R . Moreover, we compare this new method with two other approaches, in particular to one that represents a direct ...