Article

# Classes of uniformly starlike and convex functions

International Journal of Mathematics and Mathematical Sciences 01/2004; DOI: 10.1155/S0161171204402014

Source: DOAJ

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**ABSTRACT:**The purpose of the present paper is to introduce and investigate the function classes k-SP(α, β) and k-UCV(α, β) of analytic functions associated with conic regions in the open unit disk U, which generalize the function classes defined and studied in a series of earlier papers by Kanas et al. [11, 12, 13, 14]. In particular, we consider the extremal problems for each of the above-mentioned function classes. The Fekete-Szegö problem is also considered for functions in the class k-SP(α, β). Moreover, we investigate some mapping properties for each of the function classes k-SP(α, β) and k-UCV(α, β).TAIWANESE JOURNAL OF MATHEMATICS 01/2012; 16(1). · 0.66 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions belonging to the class TS(g,λ;α,β). Furthermore partial sums f n (z) of functions f(z) in the class TS(g,λ;α,β) are considered and sharp lower bounds for the ratios of real part of f(z) to f n (z) and f ' (z) to f n ' (z) are determined.Matematicki Vesnik 01/2013; 65(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**The object of the present paper is to investigate the distortion bounds for fractional calculus of functions in the class UT(Φ,Ψ,α,β) consisting of uniformly convex functions with negative coefficients. We further investigate the distortion bounds for functions in these classes under certain fractional integral operators and study their integral means properties.Southeast Asian Bulletin of Mathematics 01/2008; 32(4).

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