The Radius of Convexity of Partial Sums of Convex Functions in One Direction

被引：9

作者：

Maharana, Sudhananda ^{[1
]}

Prajapat, Jugal K. ^{[1
]}

Srivastava, Hari M. ^{[2
]}

机构：

[1] Cent Univ Rajasthan, Kishangarh 305817, Rajasthan, India

[2] Univ Victoria, Victoria, BC V8W 3R4, Canada

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES | 2017年 / 87卷 / 02期

关键词：

Analytic; Univalent; Close-to-convex; Starlike; Convex functions; Convex function in one direction; Radius of convexity; Hurwitz-Lerch zeta function;

D O I：

10.1007/s40010-017-0348-7

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we show that every section of function in a family of convex function in one direction in the open unit disk are convex in D1/2 - {z is an element of C : vertical bar z vertical bar < 1/2}. The radius 1/2 is best possible.

引用

页码：215 / 219

页数：5

共 13 条

[1]

1Ozaki S., 1941, I I. Sci.Rep. Tokyo Bunrika Daigaku. Sect., VA4, P45

[2]

3Umezawa T., 1952, J. Math. Soc. Japan, V4, P194

[3]

5Singh R., 1982, Colloq. Math., V47, P309, DOI DOI 10.4064/CM-47-2-309-314

[4] CRITERIA FOR THE EXTREMALITY OF THE KOEBE MAPPING [J].

BSHOUTY, D ;

HENGARTNER, W .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 111 (02) :403-411

[5]

Duren P. L., 1983, UNIVALENT FUNCTIONS, V259

[6] Coefficient characterizations and sections for some univalent functions [J].

Obradovic, M. ;

Ponnusamy, S. ;

Wirths, K. -J. .

SIBERIAN MATHEMATICAL JOURNAL, 2013, 54 (04) :679-696

[7] Injectivity and Star likeness of Sections of a Class of Univalent Functions [J].

Obradovic, M. ;

Ponnusamy, S. .

COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS V, 2013, 591 :195-203

[8] Radius of convexity of partial sums of functions in the close-to-convex family [J].

Ponnusamy, Saminathan ;

Sahoo, Swadesh Kumar ;

Yanagihara, Hiroshi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 95 :219-228

[9]

Robertson MS, 1944, ANN MATH, V42, P829

[10]

Srivastava H. M., 2001, Series Associated with Zeta and Related Functions

← 1 2 →