- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 5
- Fractional order mixed difference operator and its applications in angular approximation
Fractional order mixed difference operator and its applications in angular approximation
Authors : Ramazan Akgün
Pages : 1594-1610
Doi:10.15672/hujms.569410
View : 11 | Download : 3
Publication Date : 2020-10-06
Article Type : Research
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