# On Some of Classes of p- Valent, β- Uniformly Functions

## DOI:

https://doi.org/10.37375/sjfssu.v4i1.1671## Abstract

We focus on the properties of some famous analytical functions. We introduce the classes of of *p*-Valent β-uniformly Starlike functions of order α and *p* -Valent β-uniformly Convex functions of order α.` We come out with new characterization theorems and closure theorems for functions belonging to these classes. Also, we gained radius of p -Valent convexity for functions belonging to the class p-Valent β-uniformly Convex functions of order α. We insert some notes to explain the evidence of our work.

In this present paper, we are concerned with the properties of some famous analytical functions. We introduce and study the classes of *p*-Valent β-uniformly Starlike functions of order α and *p* -Valent β-uniformly Convex functions of order α and obtain some characterization theorems and closure theorems for functions belonging to these classes. Also, by this study we come out with many necessary and sufficient characterization conditions. Also we obtain radius of *p* -Valent convexity for functions belonging to the class *p*-Valent β-uniformly Convex functions of order α. In last, a remark is listed to show the evidence of the new theorems.

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*Scientific Journal for Faculty of Science-Sirte University*,

*4*(1), 45–49. https://doi.org/10.37375/sjfssu.v4i1.1671

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