Abstract
Here, we consider the approximation of functions by a large variety of max-product operators under conformable fractional differentiability and using convexity. These are positive sublinear operators. Our study relies on our general results about positive sublinear operators. We derive Jackson-type inequalities under conformable fractional initial conditions and convexity. So our approach is quantitative by obtaining inequalities where their right hand sides involve the modulus of continuity of a high-order conformable fractional derivative of the function under approximation. Due to the convexity assumptions, our inequalities are compact and elegant with small constants.
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References
Anastassiou, G.: Moments in Probability and Approximation Theory. Pitman Research Notes in Mathematics Series. Longman Group UK, New York (1993)
Anastassiou, G.: Approximation by Sublinear Operators (2017, submitted)
Anastassiou, G.: Conformable Fractional Approximation by Max-Product Operators (2017, submitted)
Anderson, D.: Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives. Contributions in Mathematics and Engineering. In Honor of Constantin Carathéodory, pp. 25–43. Springer, Berlin (2016)
Bede, B.; Coroianu, L.; Gal, S.: Approximation by Max-Product Type Operators. Springer, Heidelberg (2016)
Abu Hammad, M.; Khalil, R.: Abel’s formula and Wronskian for conformable fractional differential equations. Int. J. Differ. Equ. Appl. 13(3), 177–183 (2014)
Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
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Anastassiou, G.A. Conformable fractional approximations by max-product operators using convexity. Arab. J. Math. 7, 159–174 (2018). https://doi.org/10.1007/s40065-018-0199-3
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DOI: https://doi.org/10.1007/s40065-018-0199-3