q-Integral Operators

Ali Aral, Vijay Gupta and Ravi P. Agarwal
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Ali Aral: Kırıkkale University, Department of Mathematics
Vijay Gupta: Netaji Subhas Institute of Technology, School of Applied Sciences
Ravi P. Agarwal: Texas A&M University-Kingsville, Department of Mathematics

Chapter Chapter 3 in Applications of q-Calculus in Operator Theory, 2013, pp 73-112 from Springer

Abstract: Abstract For many years scientists have been investigating to develop various aspects of approximation results of above operators. The recent book written by Anastassiou and Gal [18] includes great number of results related to different properties of these type of operators and also includes other references on the subject. For example, in Chapter 16 of [18], Jackson-type generalization of these operators is one among other generalizations, which satisfy the global smoothness preservation property (GSPP). It has been shown in [19] that this type of generalization has a better rate of convergence and provides better estimates with some modulus of smoothness. Beside, in [22, 23], Picard and Gauss–Weierstrass singular integral operators modified by means of nonisotropic distance and their pointwise approximation properties in different normed spaces are analyzed. Furthermore, in [40, 110], Picard and Gauss Weierstrass singular integrals were considered in exponential weighted spaces for functions of one or two variables.

Keywords: Global Smoothness Preservation Property (GSPP); Singular Integral Operators; Anastassiou; Gauss Weierstrass Operators; Pointwise Convergence Results (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-6946-9_3

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