Conformable fractional approximation by max-product operators
DOI:
https://doi.org/10.24193/subbmath.2018.1.01Keywords:
positive sublinear operators, Max-product operators, modulus of continuity, conformable fractional derivative.Abstract
Here we study the approximation of functions by a big variety of Max- product operators under conformable fractional differentiability. These are positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under conformable fractional initial conditions. So our approach is quantitative by producing in- equalities with their right hand sides involving the modulus of continuity of a high order conformable fractional derivative of the function under approximation.
Mathematics Subject Classification (2010): 26A33, 41A17, 41A25, 41A36.
References
Abu Hammad, M., Khalil, R., Abel’s formula and Wronskian for conformable fractional differential equations, International J. Differential Equations Appl., 13, 3(2014), 177-183.
Anastassiou, G., Approximation by Sublinear Operators, submitted, 2017.
Anderson, D., Taylor’s formula and integral inequalities for conformable fractional derivatives, Contributions in Mathematics and Engineering, in Honor of Constantin Carath´eodory, Springer, Berlin, (2016), pp. 25-43.
Bede, B., Coroianu, L., Gal, S., Approximation by Max-Product type Operators, Springer, Heidelberg, New York, 2016.
Iyiola, O., Nwaeze, E., Some New Results on the new Conformable Fractional Calculus with Application using D’Alambert approach, Progr. Fract. Differ. Appl., 2, 2(2016), 115- 122.
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Computational Appl. Math., 264(2014), 65-70.
Lorentz, G.G., Bernstein Polynomials, Chelsea Publishing Company, New York, NY, 1986, 2nd edition.
Popoviciu, T., Sur l’approximation de fonctions convexes d’order superieur, Mathematica (Cluj), 10(1935), 49-54.
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