Article
A Subclass of Uniformly Convex Functions Associated with Certain Fractional Calculus Operator
IAENG International Journal of Applied Mathematics 08/2009; 39(3).
Source: DOAJ
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 "[10] and [11], see also [16]). and [4]) "
[Show abstract] [Hide abstract] ABSTRACT: In this paper, we obtain some subordination and superordinationpreserving results of analytic functions associated with the fractional differintegral operator U 0,z α,β,γ . Sandwichtype result involving this operator is also derived. 
 "For the choice of λ = 0, we get the result of [4] which is as follows. "
Article: Some subclasses of uniformly convex functions involving certain fractional calculus operator
[Show abstract] [Hide abstract] ABSTRACT: In this paper, we introduce a new class MT μ,γ,η(α, β, λ) of uniformly convex functions defined by a certain fractional calculus operator. Properties like coefficient estimates, growth and distortion theorems, characterization property, modified Hadamard product, inclusion property, extreme points, closure theorem of this class are studied. Futher, we discuss a class preserving integral operator, radius of starlikeness, convexity and closetoconvexity and integral mean inequality for functions in MT μ,γ,η(α, β, λ).  [Show abstract] [Hide abstract] ABSTRACT: In this paper we introduce a class of multivalent functions which is βuniformly convex in the unit disc. Characterization property exhibited and relation with other fractional calculus operators are given. Connections with the popular classes like βuniformly convex and parabolic convex functions are pointed out. Results on modified Hadamard product, extreme points, growth and distortion theorems, class preserving integral operators, region of pvalency and radius of βuniform convexity are also derived.