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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

MOHAPATRA, S. K.  and  PANIGRAHI, T.. Radius problem for the class of analytic functions based on Ruscheweyh derivative. Proyecciones (Antofagasta) [online]. 2019, vol.38, n.3, pp.537-551. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0034.

Let 𝒜 be the class of analytic functions f (z) with the normalized condition f(0) = f 0(0)−1 = 0 in the open unit disk U. Bymaking use of Ruscheweyh derivative operator, a new subclass 𝒜(β1, β2, β3, β4; λ) of f(z) ∈ 𝒜 satisfying the inequality

for some complex numbers β1, β2, β3, β4 and for some real λ > 0 is introduced. The object of the present paper is to obtain some properties of the function class 𝒜 (β1, β2, β3, β4; λ). Also the radius problems of satisfies the condition is considered.

Keywords : Analytic function; Univalent function; Ruscheweyh derivative; Cauchy-Schwarz inequality; Radius problema; Hölder inequality; 30C45; 30C50.

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