Approximation of fractional-order integrals by algebraic polynomials. I

• Date: 1999
• Main Authors: Motornyi, V. P., Моторный, В. П.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4648
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For functionsf(x) representable by an integral operator of a special form, we investigate the behavior of the second difference Δ h 2 f(x)=f(x+h)-2f(x)+f(x-h),h>0, depending on the location of a pointx on the segment [0,1].