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Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated. 1. Introduction. Let A denote the class of functions of the form f (z) = z+ ∞ n=2 a n z

Ruscheweyh'and She&Small proved the P6lya-Schoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that clos&o-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form… (More)

A class of univalent functions is defined by making use of the Ruscheweyh derivatives. This class provides an interesting transition from starlike functions to convex functions. In special cases it has close interrelations with uniformly starlike and uniformly convex functions. We study the effects of certain integral transforms and convolutions on the… (More)

By applying certain integral operators to p-valent functions we define a comprehensive family of analytic functins. The subordinations properties of this family is studied, which in certain special cases yield some of the previously obtained results.

Inequalities involving multipliers using the sequences {c n } and {d n } of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {c n } and {d n }, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many… (More)

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- ALB LUPAŞ ALINA, Jay M. Jahangiri
- 2015

Let A (p, n) = {f ∈ H(U) : f (z) = z p + ∞ j=p+n a j z j , z ∈ U }, with A (1, 1) = A. In this paper, we consider multiplier transformations I (m, λ, l) f (z) := z + ∞ j=2 1 + λ (j − 1) + l l + 1 m a j z j , where m ∈ N∪ {0}, λ, l ≥ 0. By making use of the multiplier transformation we define a new class BI(m, µ, α, λ, l) involving functions f ∈ A. Parallel… (More)