Abstract
In this paper, we introduce a new class of analytic functions defined by a new convolution operator $J_{(\lambda_{p}),(\mu _{q}),b}^{s,a,\lambda}$ which generalizes the well-known Srivastava-Attiya operator investigated by Srivastava and Attiya (Integral Transforms Spec. Funct. 18:207-216, 2007). We derive coefficient inequalities, distortion theorems, extreme points and the Fekete-Szego problem for this new function class.
Highlights
Let A denote the class of functions f (z) normalized by ∞f (z) = z + akzk, ( . ) k=which are analytic in the open unit diskU = z: z ∈ C and |z| < .A function f (z) in the class A is said to be in the class S∗(α) of starlike functions of order α in U if it satisfies the following inequality: zf (z) >α (z ∈ U; α < ). f (z)The largely investigated Srivastava-Attiya operator is defined as [ ]: Js,a(f )(z) = z +
Γ < ), where γ z is the fractional integral operator investigated by Owa and Srivastava [ ]
We systematically investigate the class S(sλ,ap,)λ,(,∗μq),b(α) of analytic functions defined above by means of the new generalized Srivastava-Attiya convolution operator J(sλ,ap,)λ,(μq),b
Summary
The largely investigated Srivastava-Attiya operator is defined as [ ] (see [ – ]): Js,a(f )(z) = z +. The function (z, s, a) involved in the right-hand side of ) is the well-known HurwitzLerch zeta function defined by A new family of λ-generalized Hurwitz-Lerch zeta functions was investigated by Srivastava [ ] (see [ – ]). For the remainder of this paper, (λ)κ denotes the Pochhammer symbol defined, in terms of the gamma function, by. Definition The H-function involved in the right-hand side of Definition The function involved in is the multiparameter extension and generalization of the Hurwitz-Lerch zeta function (z, s, a) introduced by Srivastava et al [ , p.
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