On T-neighbourhoods of Harmonic Univalent Functions

Azizi S., Ebadian A., Yalcin S.

Iranian Journal of Science and Technology, Transaction A: Science, vol.43, no.5, pp.2269-2273, 2019 (SCI-Expanded) identifier identifier


© 2019, Shiraz University.In this present paper, given a sequence T={Tn}n=2∞ consisting of positive numbers, we define the Tδ-neighbourhood of the function f= h+ g¯ ∈ H is defined as Nδ(f)={G(z):G(z)=z+∑n=2∞(Anzn+Bn¯zn¯),∑n=2∞Tn(|an-An|+|bn-Bn|)≤δ,δ≥0}.Furthermore, we investigate some problems concerning Tδ-neighbourhoods of functions in various classes of analytic functions. The results obtained here are sharp.