HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

doi:10.1007/s10473-019-0615-6

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1661-1673.doi: 10.1007/s10473-019-0615-6

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

Jacek DZIOK

Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland

收稿日期:2018-04-16 修回日期:2019-05-14 出版日期:2019-12-25 发布日期:2019-12-30
作者简介:Jacek DZIOK,E-mail:jdziok@ur.edu.pl
基金资助:
The work was supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, University of Rzeszów.

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

Jacek DZIOK

Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland

Received:2018-04-16 Revised:2019-05-14 Online:2019-12-25 Published:2019-12-30
Supported by:
The work was supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, University of Rzeszów.

摘要/Abstract

摘要： In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

关键词: harmonic functions, subordination, starlike functions, Dziok-Srivastava operator, correlated coefficients

Abstract: In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

Key words: harmonic functions, subordination, starlike functions, Dziok-Srivastava operator, correlated coefficients

中图分类号:

30C55

Jacek DZIOK. HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS[J]. 数学物理学报(英文版), 2019, 39(6): 1661-1673.

Jacek DZIOK. HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS[J]. Acta mathematica scientia,Series B, 2019, 39(6): 1661-1673.

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HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

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