DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

doi:10.1016/S0252-9602(13)60024-7

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 609-620.doi: 10.1016/S0252-9602(13)60024-7

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DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

Jacek DZIOK|Ravinder Krishna RAINA|Janusz SOKÓL

Department of Mathematics, Institute of Mathematics, University of Rzesz´ow, ul. Rejtana 16A, 35-310 Rzesz´ow, Poland；M.P. University of Agriculture and Technology, Udaipur, India；Department of Mathematics, Rzesz´ow University of Technology, Al. Powsta´nc´ow Warszawy 12, 35-959 Rzesz´ow, Poland

收稿日期:2011-09-06 修回日期:2012-08-29 出版日期:2013-05-20 发布日期:2013-05-20

DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

Jacek DZIOK|Ravinder Krishna RAINA|Janusz SOKÓL

Department of Mathematics, Institute of Mathematics, University of Rzesz´ow, ul. Rejtana 16A, 35-310 Rzesz´ow, Poland；M.P. University of Agriculture and Technology, Udaipur, India；Department of Mathematics, Rzesz´ow University of Technology, Al. Powsta´nc´ow Warszawy 12, 35-959 Rzesz´ow, Poland

Received:2011-09-06 Revised:2012-08-29 Online:2013-05-20 Published:2013-05-20

摘要/Abstract

摘要：

This article presents some new results on the class SLM of functions that are analytic in the open unit disc U = {z : |z| < 1} satisfying the conditions that

f(0) = 0, f′(0) = 1, and α （1 +zf´´(z)/f′(z)）+ (1 − α)zf′(z)/f(z) ∈p(U)
for all z ∈ U, where α is a real number and
p(z) =1 + τ ²z²/1 − τ z − τ ²z² (z ∈ U).
The number τ = (1 − √5)/2 is such that τ ² = 1 + τ . The class SLM introduced by J. Dziok, R.K. Raina, and J. Sok´o l [3, Appl. Math. Comput. 218 (2011), 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.

关键词: Univalent functions, starlike functions, subordination, Fibonacci numbers, tri-sectrix of Maclaurin, conchoid of de Sluze

Abstract:

This article presents some new results on the class SLM of functions that are analytic in the open unit disc U = {z : |z| < 1} satisfying the conditions that

Key words: Univalent functions, starlike functions, subordination, Fibonacci numbers, tri-sectrix of Maclaurin, conchoid of de Sluze

中图分类号:

30C45

Jacek DZIOK|Ravinder Krishna RAINA|Janusz SOKóL. DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS[J]. 数学物理学报(英文版), 2013, 33(3): 609-620.

Jacek DZIOK|Ravinder Krishna RAINA|Janusz SOKóL. DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS[J]. Acta mathematica scientia,Series B, 2013, 33(3): 609-620.

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DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

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