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

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 Abstract. Let T_p,n be a subclass of analytic multivalent functions of the form
f(z) = z^p + a_p+nz^p+n + a_p+n+1z^p+n+1 + . . .
for every z in the open unit disc U. Applying the fractional calculus (fractional integral and fractional derivative), A^−λ_p,nf(z) and A^λ_p,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^−λ_p,nf(z) and A^λ_p,nf(z). Also, some simple examples of results for A^−λ_p,nf(z) and A^λ_p,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.