On t-neighbourhoods of harmonic univalent functions

Abstract

In this present paper, given a sequence T = {T-n}(n=2)(infinity) consisting of positive numbers, we define the T-delta-neighbourhood of the function f = h + (g) over bar is an element of H is defined asN-delta(f) = {G(z) : G(z) = z + (n=2)Sigma(infinity) (A(n)z(n) + (B-n) over bar(z(n)) over bar),(n=2)Sigma T-infinity(n)(vertical bar a(n) - A(n)vertical bar + vertical bar b(n) - B-n vertical bar) <= delta, delta >= 0}.Furthermore, we investigate some problems concerning T-delta-neighbourhoods of functions in various classes of analytic functions. The results obtained here are sharp.