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q-Integral Operators

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Applications of q-Calculus in Operator Theory

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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.

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Authors and Affiliations

  1. Department of Mathematics, Kırıkkale University, Yahşihan, Kirikkale, Turkey

    Ali Aral

  2. School of Applied Sciences, Netaji Subhas Institute of Technology, New Delhi, India

    Vijay Gupta

  3. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, Texas, USA

    Ravi P. Agarwal

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  1. Ali Aral
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  2. Vijay Gupta
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  3. Ravi P. Agarwal
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Aral, A., Gupta, V., Agarwal, R.P. (2013). q-Integral Operators. In: Applications of q-Calculus in Operator Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6946-9_3

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