On a best extension property with respect to a linear operator^∗

^∗The first author was supported by M.U.R.S.T. (60% and 40%) and G.N.A.F.A.

Abstract

Given a linear operator on a space of continuous or square-integrable functions, a straightforward argument allows us to modify part of its components in order to obtain a best approximation type property. As a consequence, we can define a best extension of a function with respect to a linear operator and we indicates some applications to classical squences of operators.

A meaningful application consists in the approximation of the solutions of a subitable second-order differential equation perturbed with an integral term.

Keywords:

• Voronovska ja type formulas
• Integral perturbation of second order differentors
• Modified Bernstein operators

^∗The first author was supported by M.U.R.S.T. (60% and 40%) and G.N.A.F.A.

¹Department of Mathematics, Polytechnic of Bari, Via E. Oradona 4 - 70125 Bari (italy). E.mail: [email protected]

²Departamentul de matematica, Universitatea Tehnica Str. C.Daicoviciu,15, 3400 Cluj Napoca (Romania).

^∗The first author was supported by M.U.R.S.T. (60% and 40%) and G.N.A.F.A.

¹Department of Mathematics, Polytechnic of Bari, Via E. Oradona 4 - 70125 Bari (italy). E.mail: [email protected]

²Departamentul de matematica, Universitatea Tehnica Str. C.Daicoviciu,15, 3400 Cluj Napoca (Romania).

Notes

^∗The first author was supported by M.U.R.S.T. (60% and 40%) and G.N.A.F.A.

¹Department of Mathematics, Polytechnic of Bari, Via E. Oradona 4 - 70125 Bari (italy). E.mail: [email protected]

²Departamentul de matematica, Universitatea Tehnica Str. C.Daicoviciu,15, 3400 Cluj Napoca (Romania).