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q-Integral Operators

In: Applications of q-Calculus in Operator Theory

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ali Aral & Vijay Gupta & Ravi P. Agarwal, 2013. "q-Integral Operators," Springer Books, in: Applications of q-Calculus in Operator Theory, edition 127, chapter 0, pages 73-112, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-6946-9_3
    DOI: 10.1007/978-1-4614-6946-9_3
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