Abstract
In this paper, we investigate several interesting properties of a composition operator defined on the open unit ball B 0 of the Banach algebra C(T). We also consider the Noshiro-Warschawski theorem in the Banach algebra of continuous functions.MSC:30C45, 46J10.
Highlights
Introduction and definitionsThroughout this paper, C(T) denotes the Banach algebra, with sup norm, of continuous complex-valued functions defined on a compact metric space T
We note that Nikić ([ ], Definition ) defined a similar class SC without using the function φ
We investigate several geometric properties of the class SC associated with the theory of univalent functions
Summary
Introduction and definitions Throughout this paper, C(T) denotes the Banach algebra, with sup norm, of continuous complex-valued functions defined on a compact metric space T. Let A denote the class of functions φ(z) of the form φ(z) = z + anzn, Let S denote the class of all functions in A which are univalent in the unit disk U . A function φ(z) belonging to the class S is said to be convex in U if and only if zφ (z) +
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