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FullText JMA 34_08.pdf - Journal of Mathematics and Applications

FullText JMA 34_08.pdf - Journal of Mathematics and Applications

FullText JMA 34_08.pdf - Journal of Mathematics and

J o u r n a l of Mathematics and Applications No 34, pp 87-95 (2011) Inclusion relationship and Fekete-Szegö like inequalities for a subclass of meromorphic functions Dorina Răducanu and Halit Orhan and Erhan Deniz Submitted by: Jan Stankiewicz Abstract: In this paper using a differential operator, we define a new subclass of meromorphic functions. Sharp upper bounds for the functional |a 1 − µa 2 0| in this class are obtained. An inclusion property is also given. AMS Subject Classification: 30C45, 30C80. Key Words and Phrases: Univalent meromorphic function, starlike functions, convex function, differential operator, coefficient bounds. 1 Introduction Denote by Σ the class of functions of the form f(z) = 1 ∞ z + ∑ a n z n (1) COPYRIGHT c○ by Publishing Department Rzeszów University of Technology P.O. Box 85, 35-959 Rzeszów, Poland n=0 which are analytic and univalent in the punctured disk U ∗ = {z ∈ C : 0 < |z| < 1}. A function f ∈ Σ is said to be meromorphic starlike if R zf ′ (z) f(z) < 0 , z ∈ U ∗ . (2) We denote by Σ ∗ the class of all meromorphic starlike functions. A function f ∈ Σ is said to be meromorphic convex if ( R 1 + zf ′′ ) (z) f ′ < 0 , z ∈ U ∗ . (3) (z)

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