The degree of best approximation of functions via some linear operators

Humam A. Abdulrazzaq¹, Raad Falh Hasan², Abed S. A.³, Faisal Al-Sharqi^1,*

¹Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, Anbar, Iraq

²Ministry of Education, General Directorate of Education, Baghdad, Third Rusafa, Iraq

³College of Administration and Economics, Diyala University, Iraq

Emails: ahhumam1@uoanbar.edu.iq; Raadfhassanabod@gmail.com; samiaabed@uodiyala.edu.iq; faisal.ghazi@uoanbar.edu.iq

Abstract

The concentration of linear operators is unpretentious to prove in measurable space   but there is few works in weighted space, here we will include characteristics of approximate of unrestrained functions in measured space by lined operators via direct and converse approximation theorems. In addition, the relationship between modulus of softness and K- functional where, we proven are together tools equivalence.

Keywords: Approximation of functions; Linear operators; Weighted space; Modulus of smoothness; K-functional