On Continuity of Functions between Vector Metric Spaces

Abstract

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

Property (h) of Banach Lattice and Order-to-Norm Continuous Operators

“…One of the research components could be the application of relative uniform convergence to the fixed point theory on vector metric spaces. Based on [20][21][22], we could consider replacing order convergence, in the definition of vectorial convergence (see [19], Definition 2.4), with relative uniform convergence to obtain more of the properties of vectorially continuous functions (see [20], Definition 3).…”

Coupled Fixed Point Theorems in Vector b-metric Space

“…Definition 2. 16 An E-complete vector metric space Z is a vector metric space in which every E-Cauchy sequence in Z E-converges to a limit in Z.…”

Some fixed point theorems for contractive mapping in ordered vector metric spaces

“…Let us recall the vectorial continuity defined in [2]. This concept will be used throughout this paper.…”

“…They obtained Banach contraction principle and some fixed point results for these spaces [3]. Also in [2], vectorially continuous function between vector metric spaces was defined. By this concept, the continuity can be given for more general spaces.…”