Coeffcient Estimates for Certain Subclasses of Analytic and Bi-Univalent Functions

TY - JOUR

T1 - Coeffcient Estimates for Certain Subclasses of Analytic and Bi-Univalent Functions

AU - Sun, Yong

AU - Jiang, Yue Ping

AU - Rasila, Antti

N1 - Publisher Copyright: © 2015, University of Nis. All rights reserved.

PY - 2015

Y1 - 2015

N2 - For λ ≥ 0 and 0 ≤ α < 1< β, we denote by K(λ; α ; β) the class of normalized analytic functions satisfying the two sided-inequality (Equation found) where U is the open unit disk. Let (Equation found) be the class of bi-univalent functions such that f and its inverse f-1both belong to the class K(λ; α ; β). In this paper, we establish bounds for the coeffcients, and solve the Fekete-Szegő problem, for the class K(λ; α ; β). Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coeffcients of the functions in the class K∑(λ; α ; β).

AB - For λ ≥ 0 and 0 ≤ α < 1< β, we denote by K(λ; α ; β) the class of normalized analytic functions satisfying the two sided-inequality (Equation found) where U is the open unit disk. Let (Equation found) be the class of bi-univalent functions such that f and its inverse f-1both belong to the class K(λ; α ; β). In this paper, we establish bounds for the coeffcients, and solve the Fekete-Szegő problem, for the class K(λ; α ; β). Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coeffcients of the functions in the class K∑(λ; α ; β).

KW - Bi-univalent function

KW - Coeffcient bound

KW - Univalent analytic function

UR - http://www.scopus.com/inward/record.url?scp=84928944514&partnerID=8YFLogxK

U2 - 10.2298/FIL1502351S

DO - 10.2298/FIL1502351S

M3 - 文章

AN - SCOPUS:84928944514

SN - 0354-5180

VL - 29

SP - 351

EP - 360

JO - Filomat

JF - Filomat

IS - 2

ER -