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Published January 1, 2022 | Version v1
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Approximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging Operator

Creators

  • 1. Bayburt Univ, Fac Educ, Bayburt, Turkey
  • 2. Ataturk Univ, Fac Sci, Erzurum, Turkey

Description

We investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), (r = 1, 2,...), by the Hardy averaging operator A (f) (x) = 1/x integral(x)(0) f (t)dt. If the function f lies in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), it is shown that

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