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<p>In this paper, we prove the equivalence between a K-functional and a modulus of smoothness generated by Laguerre-Bessel operator on
<disp-formula>
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<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_tmmp-2022-0008_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>𝕂</mi><mo>=</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo stretchy="false">[</mo><mo>×</mo><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo stretchy="false">[</mo><mo>.</mo></mrow></math>
<tex-math>\mathbb{K} = [0, + \infty [ \times [0, + \infty [.</tex-math>
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In this paper, we prove the equivalence between a K-functional and a modulus of smoothness generated by Laguerre-Bessel operator on



𝕂=[0,+∞[×[0,+∞[.
\mathbb{K} = [0, + \infty [ \times [0, + \infty [.

Modulus of Smoothness and K-Functionals Constructed by Generalized Laguerre-Bessel Operator

Department of Mathematics, Faculty of Sciences Aïn Chock

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we prove the equivalence between a K-functional and a modulus of smoothness generated by Laguerre-Bessel operator...

Modulus of Smoothness and K-Functionals Constructed by Generalized Laguerre-Bessel Operator

Publicado en línea: 29 nov 2022

Páginas: 107 - 116

Recibido: 25 jun 2022

DOI: https://doi.org/10.2478/tmmp-2022-0008

Palabras clave
Laguerre-Bessel transform, Generalized translation operator, Jackson’s theorems, K-functional, modulus of smoothness

© 2022 Larbi Rakhimi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Modulus of Smoothness and K-Functionals Constructed by Generalized Laguerre-Bessel Operator

Publicado en línea: 29 nov 2022

Páginas: 107 - 116

Recibido: 25 jun 2022

DOI: https://doi.org/10.2478/tmmp-2022-0008

Palabras claveLaguerre-Bessel transform, Generalized translation operator, Jackson’s theorems, K-functional, modulus of smoothness

© 2022 Larbi Rakhimi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
Laguerre-Bessel transform, Generalized translation operator, Jackson’s theorems, K-functional, modulus of smoothness