Taiwanese Journal of Mathematics

SOME CLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS

Young Jae Sim, Oh Sang Kwon, Nak Eun Cho, and H. M. Srivastava

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Abstract

The purpose of the present paper is to introduce and investigate the function classes $k$-${\cal SP}(\alpha,\beta)$ and $k$-${\cal UCV} (\alpha, \beta)$ of analytic functions associated with conic regions in the open unit disk $\mathbb{U}$, which generalize the function classes defined and studied in a series of earlier papers by Kanas et al. [11, 12, 13, 14]. In particular, we consider the extremal problems for each of the above-mentioned function classes. The Fekete-Szegö problem is also considered for functions in the class $k$-${\cal SP}(\alpha,\beta)$. Moreover, we investigate some mapping properties for each of the function classes $k$-${\cal SP}(\alpha, \beta)$ and $k$-${\cal UCV}(\alpha, \beta)$.

Article information

Source
Taiwanese J. Math., Volume 16, Number 1 (2012), 387-408.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406547

Digital Object Identifier
doi:10.11650/twjm/1500406547

Mathematical Reviews number (MathSciNet)
MR2887871

Zentralblatt MATH identifier
1244.30025

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 33E05: Elliptic functions and integrals

Keywords
analytic functions univalent functions uniformly convex functions uniformly starlike functions conformal mapping principle of subordination between analytic functions Carathéodory function differential subordination Fekete-Szegö problem Hadama

Citation

Sim, Young Jae; Kwon, Oh Sang; Cho, Nak Eun; Srivastava, H. M. SOME CLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS. Taiwanese J. Math. 16 (2012), no. 1, 387--408. doi:10.11650/twjm/1500406547. https://projecteuclid.org/euclid.twjm/1500406547


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