On a family of holomorphic functions involving linear operator

• Published in: AL-Rafidain journal of computer sciences and mathematics Vol. 17; no. 1; pp. 79 - 82
• Main Authors: Khalil, Sipal, Juma, Abdul Rahman
• Format: Journal Article
• Language: Arabic; English
• Published: Mosul University 01-06-2023
• Subjects: holomorphic functions; linear operator; radius problems; starlike functions; univalent functions
• ISSN: 2311-7990; 1815-4816; 2311-7990
• DOI: 10.33899/csmj.2023.179478

The purpose of the present article is to study and introduce the family of holomorphic univalent functions defined on the open unit disk incluing the linear operators reduced by using the convolution concept between two familiar operators introduced by many authors and also studied in various families generalized by starlike and convex functions. Also, many mathematicians considered these families, our study deals with Bord distribution series, and we obtained many interesting geometric properties like the coefficient bounds of functions belonging to our family by proving the main result in characterization theorem, we obtained also the bounds of the derivative of the operators by proving the distortion theorem ,the extreme points also take into consideration and found them, the radii convexity and starlikeness are pointed out of functions belong to this family .