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Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

Mishra, A. K., Gochhayat, P. (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15By making use of the fractional differential operator Ω^λz (0 ≤ λ < 1) due to Owa and Srivastava, a new subclass of univalent functions denoted by k−SPλ (0 ≤ k < ∞) is introduced. The class k−SPλ unifies the concepts of k-uniformly convex functions and k-starlike functions. Certain basic properties of k − SPλ such as inclusion theorem, subordination theorem, growth theorem and class preserving transforms are studied.*...

Approximate and L p Peano derivatives of nonintegral order

J. Marshall Ash, Hajrudin Fejzić (2005)

Studia Mathematica

Let n be a nonnegative integer and let u ∈ (n,n+1]. We say that f is u-times Peano bounded in the approximate (resp. L p , 1 ≤ p ≤ ∞) sense at x ∈ ℝ m if there are numbers f α ( x ) , |α| ≤ n, such that f ( x + h ) - ∑ | α | ≤ n f α ( x ) h α / α ! is O ( h u ) in the approximate (resp. L p ) sense as h → 0. Suppose f is u-times Peano bounded in either the approximate or L p sense at each point of a bounded measurable set E. Then for every ε > 0 there is a perfect set Π ⊂ E and a smooth function g such that the Lebesgue measure of E∖Π is less than ε and f = g on Π....

Approximating real Pochhammer products: a comparison with powers

Vito Lampret (2009)

Open Mathematics

Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.

Approximation of set-valued functions with compact images-an overview

Nira Dyn, Elza Farkhi (2006)

Banach Center Publications

Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing degree, and the Schoenberg operators, when represented as spline subdivision schemes, converge to set-valued...

Approximation of the Stieltjes integral and applications in numerical integration

Pietro Cerone, Sever Silvestru Dragomir (2006)

Applications of Mathematics

Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.

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