Publication Details:
Journal or Publication Title:
Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
Approximation by Some Singular Operators Type of Functions from a Generalized Zygmund Space
Creator:
Krasniq, Xhevat ; Mohapatra, Ram
Contributor(s):
Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
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Uncontrolled Keywords:
Degree of Approximation ; Singular Integrals ; Zygmund Modulus of Continuity ; Generalized Zygmund Class ; Generalized Minkowski Inequality
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Abstract:
This study continues previous research on the approximation of functions by means of singular integrals. We begin by introducing the truncated Picard singular integral. Subsequently, using this integral along with the classical Picard--Cauchy and Gauss--Weierstrass singular integrals, we establish the orders of approximation for functions belonging to a generalized Zygmund space, both in the L p -norm and in the corresponding norm of the generalized Zygmund space.
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General note:
Electronic Open Access Publication of the National Academy of Sciences of Armenia