On Fully-Convex Harmonic Functions and their Extension

Shahpour Nosrati, Ahmad Zireh

Abstract


‎Uniformly convex univalent functions that introduced by Goodman‎, ‎maps every circular arc contained in the open unit disk with center in it into a convex curve‎. ‎On the other hand‎, ‎a fully-convex harmonic function‎, ‎maps each subdisk $|z|=r<1$ onto a convex curve‎. ‎Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also‎. ‎In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution‎. 

Keywords


Uniformly convex function‎; ‎Fully-Convex function‎; ‎Harmonic function‎; ‎Convolution‎

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DOI: http://dx.doi.org/10.5269/bspm.v38i2.34684



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ISSN 0037-8712 (print) and ISSN 2175-1188 (on-line)

 

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