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In this paper, we determine sharp lower bounds for Re { f(z)∗ψ(z) fn(z)∗ψ(z) } and Re { fn(z)∗ψ(z) f(z)∗ψ(z) } . We extend the results of ([1] – [5]) and correct the conditions for the results of Frasin [2, Theorem 2.7], [1, Theorem 2], Rosy et al. [4, Theorems 4.2 and 4.3], as well as Raina and Bansal [3, Theorem 6.2].

- Saurabh Porwal
- 2008

The class of univalent harmonic functions on the unit disc satisfying the condition ∑∞ k=2 (k m − αk)(|ak|+ |bk|) ≤ (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 theorems… (More)

- S. Porwal, K. K. Dixit
- 2011

Let φ (z) be a fixed analytic and univalent function of the form φ(z) = z + ∑∞ k=2 ckz k and Hφ (ck, δ) be the subclass consisting of analytic and univalent functions f of the form f(z) = z + ∑∞ k=2 akz k which satisfy the inequality ∑∞ k=2 ck |ak| ≤ δ. In this paper, we determine the sharp lower bounds for Re { Dpf(z) Dfn(z) } and Re { Dfn(z) Dpf(z) } ,… (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 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.

- Saurabh Porwal
- Int. J. Math. Mathematical Sciences
- 2012

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)

- Saurabh Porwal
- 2011

A recent result of Yalcin [9] appeared in Applied Mathematics Letters (2005), concerning the convolution of two harmonic univalent functions in class SH(m,n, α) is improved. AMS (MOS) Subject Classification Codes: 30C45

- SAURABH PORWAL
- 2013

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)

This paper devoted to the study of incomplete Mittag-Leffler function and some of its properties in terms of incomplete Wright function. 2000 Mathematics Subject Classification: 33E12, 33B15, 11S80.

The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results… (More)