Acta mathematica scientia, Series B >
DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS
Received date: 2011-09-06
Revised date: 2012-08-29
Online published: 2013-05-20
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.
Jacek DZIOK|Ravinder Krishna RAINA|Janusz SOKóL . DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 609 -620 . DOI: 10.1016/S0252-9602(13)60024-7
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