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)
For functions p analytic in the open unit disc U = {z : |z| < 1} with the normaliza-tion p(0) = 1, we consider the families ᏼ[A, −1], −1 < A ≤ 1, consisting of p such that p(z) is subordinate to (1+Az)/(1−z) in U and ᏼ(1,b), b > 0, consisting of p, which have the disc formulation |p −1| < b in U. We then introduce subordination criteria for the choice of(More)