Coefficient estimates for starlike and convex functions associated with cosine function

被引：7

作者：

Marimuthu, Krishnan ^{[1
]}

Uma, Jayaraman ^{[1
]}

Bulboaca, Teodor ^{[2
]}

机构：

[1] SRM Inst Sci & Technol, Coll Engn & Technol, Dept Math, Kattankulathur 603203, Tamilnadu, India

[2] Babes Bolyai Univ, Fac Math & Comp Sci, Cluj Napoca 400084, Romania

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2023年 / 52卷 / 03期

关键词：

analytic functions; subordination; cosine function; coefficient bounds; Hankel determinant; Zalcman functional; logarithmic coefficients; successive coefficients difference; HANKEL DETERMINANT; ZALCMAN CONJECTURE; RADIUS PROBLEMS; INEQUALITIES;

D O I：

10.15672/hujms.1133174

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with the new classes S*cos and S ccos of starlike and convex functions, respectively, associated with the cosine function. We give initial coefficient bounds for the first seven coefficients of the functions that belong to these classes, and we evaluate the upper bounds for the Hankel determinant of order three and four. We found the upper bound of Zalcman functional for the above mentioned classes for the cases n = 3 and n = 4, showing that the Zalcman conjecture holds for these values. Moreover, we determined lower and upper bounds for the difference |al| - |a3| of the coefficients for the functions that belong to these classes.

引用

页码：596 / 618

页数：23

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