Search

The aim of this paper is to study the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite collection of generalized cyclic Γ-contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper we study the space of strongly Lipschitz (lp,lq)-factorable operators between metric spaces and a Banach spaces. In particular, a factorization of this class through lp and lq spaces is given. We show that this type of operators fits in the theory of composition a-Banach Lipschitz operator ideal. As a special case, we get a Lipschitz version of weakly p-nuclear operators. [ABSTRACT FROM AUTHOR]

Consider the ring M∘(X,μ) of functions which are discontinuous on a set of measure zero which is introduced and studied extensively in [2]. In this paper, we introduce a ring B1(X,μ) of functions which are pointwise limits of sequences of functions in Mo(X,μ'). We study various properties of zero sets, B1(X, p)-separated and B1(X, p)-embedded subsets of B1(X,μ) and also establish an analogous version of Urysohn's extension theorem. We investigate a connection between ideals of B1(X,μ) and ZB-filters on X. We study an analogue of Gelfand-Kolmogoroff theorem in our setting. We define real maximal ideals of B1(X,μ) and establish the result |RMax(Mo(X,μ))| = |RMax(B1(X, μ))|, where RMax(M∘(X, μ)) and RMax(B1(X, μ)) are the sets of all real maximal ideals of M∘(X,μ) and B1(X,μ), respectively. [ABSTRACT FROM AUTHOR]

In the present paper we define the degree of nondensifiability (DND for short) of a bounded linear operator T on a Banach space and analyze its properties and relations with the Hausdorff measure of noncompactness (MNC for short) of T. As an application of our results, we have obtained a formula to find the essential spectral radius of a bounded operator T on a Banach space as well as we have provided the best possible lower bound for the Hyers-Ulam stability constant of T in terms of the aforementioned DND. [ABSTRACT FROM AUTHOR]

Given a uniform space (X, U), we denote by F*(X) to the family of fuzzy sets u in (X, U) such that u is normal and upper semicontinu-ous. Let UE be the endograph uniformity on F*(X). In this paper, we mainly characterize totally bounded and compact subsets in the uniform space (F*(X), UE). [ABSTRACT FROM AUTHOR]

In this paper new notions of dimensions for ideal topological spaces are inserted, called *-quasi covering dimension and ideal quasi covering dimension. We study several of their properties and investigate their relations with types of covering dimensions like the-covering dimension and the ideal covering dimension. [ABSTRACT FROM AUTHOR]

This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results. [ABSTRACT FROM AUTHOR]

Recently, Karapinar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

This paper continues a series discussing flaws in published assertions concerning fixed points in digital images. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalizations of the concept of MR-Kannan type contractions and utilize those conditions to derive new fixed point theorems under both contractive and non-contractive conditions. Our approach enhances various existing results related to enriched mappings. [ABSTRACT FROM AUTHOR]

The paper deals with some further results concerning the class of two-Lipschitz operators. We prove first an isometric isomorphism identification of two-Lipschitz operators and Lipschitz operators. After defining and characterizing the adjoint of a two-Lipschitz operator, we prove a Schauder type theorem on the compactness of the adjoint. We study the extension of two-Lipschitz operators from the cartesian product of two complemented subspaces of a Banach space to the cartesian product of whole spaces. Also, we show that every two-Lipschitz functional defined on the cartesian product of two pointed metric spaces admits an extension with the same two-Lipschitz norm under some requirements on domaine spaces. [ABSTRACT FROM AUTHOR]