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Applications of certain linear operators in the theory of analytic functions

H. M. Srivastava (1991)

Annales Polonici Mathematici

The object of the present paper is to illustrate the usefulness, in the theory of analytic functions, of various linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on.

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.*...

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 by q -Bernstein type operators

Zoltán Finta (2011)

Czechoslovak Mathematical Journal

Using the q -Bernstein basis, we construct a new sequence { L n } of positive linear operators in C [ 0 , 1 ] . We study its approximation properties and the rate of convergence in terms of modulus of continuity.

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