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GEOMETRIC AND APPROXIMATION PROPERTIES OF GENERALIZED SINGULAR INTEGRALS IN THE UNIT DISK
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 Title & Authors
GEOMETRIC AND APPROXIMATION PROPERTIES OF GENERALIZED SINGULAR INTEGRALS IN THE UNIT DISK
Anastassiou George A.; Gal Sorin G.;
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 Abstract
The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.
 Keywords
generalized complex singular integrals;Jackson-type estimates;global smoothness preservation;shape preserving properties;approximation of vector-valued functions;
 Language
English
 Cited by
1.
Convolution Properties for Certain Classes of Analytic Functions Defined byq-Derivative Operator, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
2.
Some Subordination Results onq-Analogue of Ruscheweyh Differential Operator, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
3.
Certain Properties of Some Families of Generalized Starlike Functions with respect toq-Calculus, Abstract and Applied Analysis, 2016, 2016, 1  crossref(new windwow)
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