Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function

G. Murugusundaramoorthy, K. Uma

Abstract


Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by \(TS^\mu_b(\alpha, \beta, \gamma)\) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class \(TS^\mu_b(\alpha, \beta, \gamma)\). In particular, we obtain integral means inequalities for the function \(f(z)\) belongs to the class \(TS^\mu_b(\alpha, \beta, \gamma)\) in the unit disc.

Keywords


Univalent; starlike, convex; uniformly convex; uniformly starlike; Hadamard product; integral means; Hurwitz-Lerch Zeta function

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References


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DOI: http://dx.doi.org/10.2478/v10062-010-0015-9
Date of publication: 2016-07-29 10:39:56
Date of submission: 2016-07-28 22:40:21


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