TL;DR
This paper introduces concepts of vectorial and topological continuity in vector metric spaces, explores spaces of such functions, and discusses fundamental classes and extension theorems for vector-valued functions.
Contribution
It develops new notions of continuity in vector metric spaces and provides foundational results on classes and extensions of vector-valued functions.
Findings
Defined vectorial and topological continuity in vector metric spaces
Characterized spaces of vector-valued functions
Established extension theorems for these functions
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.
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Taxonomy
TopicsFixed Point Theorems Analysis · Functional Equations Stability Results · Advanced Banach Space Theory