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The class of univalent harmonic functions on the unit disc satisfying the condition ∞ k=2 (k m − αk n)(|a k | + |b k |) ≤ (1 − α)(1 − |b1|) is given. Sharp coefficient relations and distortion theorems are given for these functions. In this paper we find that many results of Özturk and Yalcin [5] are incorrect. Some of the results of this paper correct the(More)
In wireless communication, using ad-hoc networking any user desiring to communicate with each other can form a temporary network, without any form of centralized administration. Each node participating in the network is mobile and can be connected dynamically in an arbitrary manner. All nodes of these networks behave as routers and take part in discovery(More)
The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here(More)
Let φ (z) be a fixed analytic and univalent function of the form φ(z) = z + ∞ k=2 c k z k and H φ (c k , δ) be the subclass consisting of analytic and univalent functions f of the form f (z) = z + ∞ k=2 a k z k which satisfy the inequality ∞ k=2 c k |a k | ≤ δ. In this paper, we determine the sharp lower bounds for Re D p f (z) D p fn(z) and Re D p fn(z) D(More)
A continuous complex-valued function f u iv is said to be harmonic in a simply connected domain D if both u and v are real harmonic in D. In any simply-connected domain we can write f h g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and(More)
The purpose of the present paper is to study some results involving coefficient conditions, extreme points, distortion bounds, convolution conditions and convex combination for a new class of harmonic multivalent functions in the open unit disc. Relevant connections of the results presented here with various known results are briefly indicated.