Equivalence of K-Functionals and Modulus of Smoothness Generated by The $ q $-Rubin Operator

Authors

  • Sami Rebhi

DOI:

https://doi.org/10.5644/SJM.15.01.05

Keywords:

q2-analogue differential Operator, q-Rubin transform, q- translation Operator, K-functionals, Modulus of Smoothness

Abstract

In this paper, the equivalence between K-functionals and modulus of smoothness tied to a $ q $-Rubin operator was studied.

 

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References

R. P. Agarwal, M. Meehan and D. O'Regan, Fixed Point Theory and Applications, Cambridge Univ. Press, United Kingdom, 2001.

P. L. Butzer, H. Behrens, Semi-groups of operators and approximation, Springer, Berlin, Heidelbarg, New York, 1967.}

M. M. Chaffar, N. Bettaibi, A. Fitouhi, Sobolev Type Spaces Associated With The q-Rubin's Operator, LE Matematiche, Fasc. I, pp. 37-56 (2014).}

R. W. Corley, Some hybrid fixed point theorems related to optimization, J. Math. Anal. Appl., 120 (1980), 528--532.

F. H. Jackson, On a q-Definite Integrals, Q. J. Pure Appl. Math. 41, 193-203 (1910).}

Peetre J, A theory of interpolation of normed spaces, Notas Mat. 39 (1963, 1968).

M. Imdad, A. Ahmad and S. Kumar, On nonlinear nonself hybrid contractions, Rad. Mat., 10 (2) (2001), 233--244.

R. L. Rubin, A $ q^{2}-$Analogue Operator for $ q^{2}-$analogue Fourier Analysis, J. Math. Analys. Appl. 212 , 571-582 (1997).

R. L. Rubin, Duhamel Solutions of non-Homogenous $ q^{2}-$analogue Wave Equations, Proc. of Amer. Math.Soc. V 135 (3), 777-785 (2007).

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Published

07.03.2022

How to Cite

Rebhi, S. . (2022). Equivalence of K-Functionals and Modulus of Smoothness Generated by The $ q $-Rubin Operator. Sarajevo Journal of Mathematics, 15(1), 49–56. https://doi.org/10.5644/SJM.15.01.05

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Articles