Jay M. Jahangiri

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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)
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)
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)