A modified averaging operator with some applications
A modified averaging operator with some applications
The paper presents a new approach to the conventional averaging in which the role of boundary values is considered in a more detailed way. It results in a new weighted local averaging operator (WLAO) taking into account the particular role of boundary values. A remarkable feature of WLAO is that this operator contains a parameter of boundary regulation p and depends on a local value h of the integration domain. By varying these two parameters one can regulate the obtained approximate solutions i