Subclasses of $k$-uniformly convex and $k$-starlike functions defined by S\u{a}l\u{a}gean operator
Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 169-182
Published online January 1, 2011
Bilal \c{S}eker, Mugur Acu, and Sevtap S\"{u}mer Eker
Batman University, Str. Dr. I. Ratiu 5-7, Dicle University
Abstract : The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of $k$-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.
Keywords : S\u{a}l\u{a}gean operator, $k$-starlike, $k$-uniformly convex, coefficient inequalities, distortion inequalities, extreme points, integral means, fractional derivative, integral operators
MSC numbers : Primary 30C45
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