Fractional order mixed difference operator and its applications in angular approximation

Authors : Ramazan AKGÜN

Pages : 1594-1610

Doi:10.15672/hujms.569410

View : 24 | Download : 14

Publication Date : 2020-10-06

Article Type : Research Paper

Abstract :Lebesgue spaces are considered with Muckenhoupt weights. Fractional order mixed difference operator is investigated to obtain mixed fractional modulus of smoothness in these spaces. Using this modulus of smoothness we give the proof of direct and inverse estimates of angular trigonometric approximation. Also we obtain an equivalence between fractional mixed modulus of smoothness and fractional mixed K-functional. ********************************************************** **********************************************************
Keywords : Difference Operator, Lebesgue spaces, Muckenhoupt weights, Angular Trigonometric Approximation, mixed modulus of smoothness