Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method
| Autor: | Mohammad Mursaleen, Vishnu Narayan Mishra, Abhishek Mishra |
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| Rok vydání: | 2020 |
| Předmět: |
Lipschitz class
Almost Euler summability means 01 natural sciences Combinatorics symbols.namesake Double Fourier series Modulus of continuity Beta (velocity) 0101 mathematics Fourier series Mathematics Double Hausdorff matrix summability Algebra and Number Theory Partial differential equation lcsh:Mathematics Applied Mathematics Cesàro summability 010102 general mathematics Hausdorff space lcsh:QA1-939 010101 applied mathematics Ordinary differential equation Euler's formula symbols Trigonometry Generalized Lipschitz class Analysis |
| Zdroj: | Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-10 (2020) |
| ISSN: | 1687-1847 |
| DOI: | 10.1186/s13662-020-03124-8 |
| Popis: | In this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means. |
| Databáze: | OpenAIRE |
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