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JOURNALS // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Archive

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015 Number 3, Pages 35–49 (Mi basm401)

Research articles

Certain classes of $p$-valent analytic functions with negative coefficients and $(\lambda,p)$-starlike with respect to certain points

Adnan Ghazy Alamoush, Maslina Darus

School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia

Abstract: In this article, we consider classes $S_{s,\lambda}^*(p,\alpha,\beta)$, $S_{c,\lambda}^*(p,\alpha,\beta)$, and $S_{sc,\lambda}^*(p,\alpha,\beta)$ of p-valent analytic functions with negative coefficients in the unit disk. They are, respectively, $(\lambda,p)$-starlike with respect to symmetric points, $(\lambda,p)$-starlike with respect to conjugate points, and $(\lambda,p)$-starlike with respect to symmetric conjugate points. Necessary and sufficient coefficient conditions for functions $f$ belonging to these classes are obtained. Several properties such as the coefficient estimates, growth and distortion theorems, extreme points, radii of starlikeness, convexity, and integral operator are studied.

Keywords and phrases: p-valent functions, univalent functions, Salagean operator, starlike with respect to symmetric points.

MSC: 30C45

Received: 10.05.2015

Language: English



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