Approximation properties of Bernstein`s singular integrals in variable exponent Lebesgue spaces on the real axis

Authors : Ramazan AKGÜN

Pages : 1059-1079

Doi:10.31801/cfsuasmas.1056890

View : 11 | Download : 7

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :In generalized Lebesgue spaces $L^{pinsert ignore into journalissuearticles values(.);}$ with variable exponent $pinsert ignore into journalissuearticles values(.);$ defined on the real axis, we obtain several inequalities of approximation by integral functions of finite degree. Approximation properties of Bernstein singular integrals in these spaces are obtained. Estimates of simultaneous approximation by integral functions of finite degree in $L^{pinsert ignore into journalissuearticles values(.);}$ are proved.
Keywords : Modulus of smoothness, simultaneous approximation, Bernstein singular integral, forward Steklov mean, mollifiers, Jackson inequality, entire integral functions of finite degree