On Classes of Analytic Functions Associated by a Parametric Linear Operator in a Complex Domain: On Classes of Analytic Functions Associated by a Parametric Linear Operator

Rabha W.  Ibrahim; Adem  Kilicman; Zainab E.  Abdulnaby

Authors

Rabha W. Ibrahim Faculty of Computer Science and Information Technology, University of Malaya, 50603, Malaysia
Adem Kilicman Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
Zainab E. Abdulnaby Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.Department of Mathematics, College of Science, Al-Mustansiriyah University, Baghdad, Iraq

Keywords:

analytic functions, univalent function, starlike function, convex function, bounded turning function, Laguerre polynomial, convolution (or Hadamard product), Riemann zeta function

Abstract

The present paper deals with some geometric classes of analytic functions, such as starlike, convex and bounded turning property in a complex domain. These classes are defined by a new linear operator in the normalized space of analytic functions. The linear operator is introduced by a convolution of Szego function involving parametric coefficients type Laguerre polynomial, with the normalized function. Sufficient conditions on this operator are illustrated to study the geometric properties. Our tool is based on some recent results in this direction. The main strategy for this work is to provide parametric functional inequalities in the open unit disk.

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On Classes of Analytic Functions Associated by a Parametric Linear Operator in a Complex Domain