Volume 7, Issue 4, August 2018, Page: 45-62
On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator
Ozokeraha Christiana Funmilayo, Department of Statistics, Delta State Polytechnic, Oghara, Nigeria
Received: Jul. 31, 2018;       Accepted: Sep. 18, 2018;       Published: Nov. 6, 2018
DOI: 10.11648/j.pamj.20180704.11      View  115      Downloads  7
Abstract
In recent times, the study of analytic functions has been useful in solving many problems in mechanics, Laplace equation, electrostatics, etc. An analytic function is said to be univalent in a domain if it does not take the same value twice in that domain while an analytic function is said to be p-valent in a domain if it does not take the same value more than p times in that domain. Many researches on properties of p-valent functions using Salagean, Al Oboudi and Opoola differential operators have been reviewed. The aim of this research is to obtain the properties of new subclasses of p-valent functions defined by Salagean differential operator and its objectives are to obtain new subclasses of p-valent functions and the necessary properties for the new subclasses. This research will be a contribution to knowledge in geometric function theory and provide new tools of applications in fluid dynamics and differential equations. This paper introduces new subclasses of p – valent functions defined by Al –Oboudi differential operator. Finally, the paper studies some interesting results including subordination, coefficient inequalities, starlikeness and convexity conditions, Hadamard product and certain properties of neighbourhoods of the new subclasses of p-valent functions. Theorems were used to establish certain conditions of the new subclasses of p-valent functions.
Keywords
P-Valent Functions, Analytic Functions, Differential Operator, Subordination
To cite this article
Ozokeraha Christiana Funmilayo, On a Subclass of P-Valent Functions Defined by a Generalized Salagean Operator, Pure and Applied Mathematics Journal. Vol. 7, No. 4, 2018, pp. 45-62. doi: 10.11648/j.pamj.20180704.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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