An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination

被引：156

作者：

Srivastava, H. M. ^{[1
]}

Attiya, A. A.

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[2] Univ Mansoura, Fac Sci, Dept Math, Mansoura 35516, Egypt

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2007年 / 18卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

analytic functions; univalent functions; convex functions; starlike functions; differential subordination; Hurwitz-Lerch Zeta function; Riemann and Hurwitz (or generalized) zeta functions; polylogarithmic function; Jung-Kim-Srivastava integral operator; Hadamard product (or convolution); mutiplier transformations; Koebe function of order alpha;

D O I：

10.1080/10652460701208577

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main object of this article is to introduce and investigate an integral operator J(s,b)(f) defined, by using the Hurwitz-Lerch Zeta function, on the various subclasses of the class of normalized analytic functions f in the open unit disk U. Using the technique of differential subordination, an interesting property of the general integral operator J(s,b)(f) is obtained. Some applications of the results presented here are also considered.

引用

页码：207 / 216

页数：10

共 15 条

[1] Functions which map the interior of the unit circle upon simple regions. [J].

Alexander, JW .

ANNALS OF MATHEMATICS, 1915, 17 :12-22

[2]

[Anonymous], 2000, SERIES PURE APPL MAT

[3] CONVEX AND STARLIKE UNIVALENT FUNCTIONS [J].

BERNARDI, SD .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 135 (JAN) :429-&

[4] Certain families of series associated with the Hurwitz-Lerch Zeta function [J].

Choi, JS ;

Srivastava, HM .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 170 (01) :399-409

[5] Asymptotic expansions of the Hurwitz-Lerch zeta function [J].

Ferreira, C ;

López, JL .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 298 (01) :210-224

[6] DUAL OF AN INEQUALITY OF HARDY AND LITTLEWOOD AND SOME RELATED INEQUALITIES [J].

FLETT, TM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 38 (03) :746-&

[7] THE HARDY SPACE OF ANALYTIC-FUNCTIONS ASSOCIATED WITH CERTAIN ONE-PARAMETER FAMILIES OF INTEGRAL-OPERATORS [J].

JUNG, IB ;

KIM, YC ;

SRIVASTAVA, HM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 176 (01) :138-147

[8]

Libera R. J., 1969, P AM MATH SOC, V135, P429

[9] Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations [J].

Lin, SD ;

Srivastava, HM .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (03) :725-733

[10] A linear operator and strongly starlike functions [J].

Liu, JL .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2002, 54 (04) :975-981

← 1 2 →