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6: Paper Source PDF document

Paper's Title:

Multivalent Harmonic Mappings Convoluted With a Multivalent Analytic Function

Author(s):

Om P. Ahuja and Özlem Güney

Kent State University, Department of Mathematical Sciences,
14111, Claridon-Troy Road, Burton, Ohio 44021,
U.S.A.
oahuja@kent.edu

University of Dicle, Department of Mathematics,
Faculty of Science and Art, 21280 Diyarbakir,
Turkey
ozlemg@dicle.edu.tr

Abstract:

The object of this paper is to study certain geometric properties of a family of multivalent harmonic mappings in the plane convoluted with a multivalent analytic function in the open unit disc.



1: Paper Source PDF document

Paper's Title:

On Certain Classes of Harmonic Univalent Functions Based on Salagean Operator

Author(s):

G. Murugusundaramoorthy, Thomas Rosy, and B. A. Stephen

Department of Applied Mathematics and Informatics,
Department of Mathematics, Vellore Institute of Technology,
Deemed University, Vellore - 632014, India.
gmsmoorthy@yahoo.com
 

Department of Applied Mathematics and Informatics,
Department of Mathematics, Madras Christian College,
Chennai - 600059, India.
drthomasrosy@rediffmail.com 

Abstract:

We define and investigate a class of complex-valued harmonic univalent functions of the form f = h + g using Salagean operator where h and g are analytic in the unit disc U = { z : |z| < 1 }. A necessary and sufficient coefficient conditions are given for functions in these classes. Furthermore, distortion theorems, inclusion relations, extreme points, convolution conditions and convex combinations for this family of harmonic functions are obtained.



1: Paper Source PDF document

Paper's Title:

Fekete-Szegö Problem for Univalent Functions with Respect to k-Symmetric Points

Author(s):

K. Al-Shaqsi and M. Darus

School of Mathematical Sciences, Faculty of Science and Technology,
University Kebangsaan Malaysia,
Bangi 43600 Selangor D. Ehsan,
Malaysia
ommath@hotmail.com
maslina@ukm.my 


Abstract:

In the present investigation, sharp upper bounds of |a3- μa22| for functions f(z) = z + a2z2 + a2z3 + ... belonging to certain subclasses of starlike and convex functions with respect to k-symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete- Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.


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