New Applications of the Bernardi Integral Operator

Mathematics

H.Özlem Güney¹  Shigeyoshi Owa² 

[1] Department of Mathematics, Faculty of Science Dicle University, 21280 Diyarbakır, Turkey;“1 Decembrie 1918" University Alba Iulia, 510009 Alba-Iulia, Romania;

关键词: analytic p-valent function;    Bernardi integral operator;    Libera integral operator;    fractional integral;    gamma function;    Miller–Mocanu lemma;   

DOI  :  10.3390/math8071180

来源: DOAJ

【 摘 要 】

Let $A(p,n)$ be the class of $f\left(z\right)$ which are analytic p-valent functions in the closed unit disk $\overline{\mathbb{U}}=\left\{z\in \mathbb{C}:\left|z\right|\le 1\right\}$ . The expression $B_{-m-\lambda }f\left(z\right)$ is defined by using fractional integrals of order $\lambda$ for $f\left(z\right)\in A(p,n).$ When $m=1$ and $\lambda =0,$ $B_{-1}f\left(z\right)$ becomes Bernardi integral operator. Using the fractional integral $B_{-m-\lambda }f\left(z\right),$ the subclass $T_{p,n}\left({\alpha }_s,\beta ,\rho ;m,\lambda \right)$ of $A(p,n)$ is introduced. In the present paper, we discuss some interesting properties for $f\left(z\right)$ concerning with the class $T_{p,n}\left({\alpha }_s,\beta ,\rho ;m,\lambda \right).$ Also, some interesting examples for our results will be considered.

【 授权许可】

Unknown