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Generalizations of the Alexander integral operator for Analytic Multivalent Functions

H. Özlem Güney (1) and Shigeyoshi Owa (2)

(1) Department of Mathematics, Faculty of Science, Dicle University, Diyarbakır, Turkiye

Email address: ozlemg@dicle.edu.tr


(2) Honorary Professor ”1 Decembrie 1918”, University Alba Iulia, Romania

Email address: shige21@ican.zaq.ne.jp

Doi : https://doi.org/10.47013/15.4.6

Cited by : Jordan J. Math & Stat., 15 (4A) (2022), 871 - 894


Received on: May 17, 2021;                                           Accepted on: June 1, 2022

 Abstract. Let Tp,n be a subclass of analytic multivalent functions of the form
f(z) = zp + ap+nzp+n + ap+n+1zp+n+1 + . . .
for every z in the open unit disc U. Applying the fractional calculus (fractional integral and fractional derivative), A−λp,nf(z) and Aλp,nf(z) which are generalizations of the Alexander integral operator are introduced. The object of present paper is to discuss some interesting properties of A−λp,nf(z) and Aλp,nf(z). Also, some simple examples of results for A−λp,nf(z) and Aλp,nf(z) are shown. To give some simple examples is very important for the research of mathematics.

Keywords: Analytic function, fractional derivative, fractional integral, Alexander integral operator, dominant, subordination.