Approximation by matrix transforms in generalized grand Lebesgue spaces with variable exponent

Abstract

The approximation properties of the matrix transforms, constructed via lower triangular matrices, satisfying some additional conditions, in the generalized grand Lebesgue spaces with variable exponent are studied and the appropriate rates of approximation are estimated.

Keywords:

• Trigonometric approximation
• matrix transforms
• modulus of smoothness
• grand variable exponent Lebesgue spaces
• Lipschitz classes

Mathematical Subject Classification (2010):

• 41A10
• 42A10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Balikesir University grant 2017/032-A: ‘Approximation by Matrix Transforms in Generalized Grand Lebesgue Spaces with Variable Exponent’.