On a general approach to some problems of approximation of operators

TL;DR

This paper introduces a general framework for solving various operator approximation problems and demonstrates its effectiveness through multiple examples, including deriving Ostrowski type inequalities.

Contribution

It presents a unified scheme for operator approximation problems applicable in broad settings, simplifying derivations of known inequalities.

Findings

Many Ostrowski type inequalities can be derived using standard methods within this new framework.

The proposed scheme is versatile and applicable to a wide range of approximation problems.

The approach simplifies existing proofs and provides a systematic way to obtain inequalities.

Abstract

In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in the area of Ostrowski type inequalities can be obtained by standard arguments.