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May  2015, 14(3): 743-757. doi: 10.3934/cpaa.2015.14.743

## General types of spherical mean operators and $K$-functionals of fractional orders

 1 Departamento de Matemática, Universidade de São Paulo (ICMC - USP), São Carlos, SP 13560-970, Brazil 2 Department of Mathematics, Missouri State University, Springfield, MO 65804, United States

Received  March 2014 Revised  September 2014 Published  March 2015

We design a general type of spherical mean operators and employ them to approximate $L_p$ class functions. We show that optimal orders of approximation are achieved via appropriately defined K-functionals of fractional orders.
Citation: Thaís Jordão, Xingping Sun. General types of spherical mean operators and $K$-functionals of fractional orders. Communications on Pure & Applied Analysis, 2015, 14 (3) : 743-757. doi: 10.3934/cpaa.2015.14.743
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