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In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric…
The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.
Here we have studied the ideas of $ sg_\lambda,s\lambda$ and $ s\beta_\lambda $-closed sets and investigated some of their properties in generalized topological spaces. We have also studied some low separation axioms namely $ s\lambda…
In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
We study open sets $\mathcal{P}$ in normed spaces $X$ attaining a large volume while avoiding pairs of points at integral distance. The proposed task is to find sharp inequalities for the maximum possible $d$-dimensional volume. This…
Let a $R$-body be a closed set, complement of union of open balls of radius $R$ in the Euclidean space. Properties generalizing similar ones for convex sets are proved for the family of $R$-bodies; properties for the family of sets…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…
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…
The aim of this review is to present an overview over available models and approaches to non-commutative gauge theory. Our main focus thereby is on gauge models formulated on flat Groenewold-Moyal spaces and renormalizability, but we will…
In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of $\mathbb R^n$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. Also, space limitation does not…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…