A new view of some operators and their properties in terms of the Non-Newtonian Calculus

Abstract

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of substraction and addition into division and multiplication, respectively and thus established a new calculus, called Non-Newtonian Calculus. So in this paper, it is investigated to a new view of some operators and their properties in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.

Keywords

• bounded operators
• hilbert space
• non-newtonian calculus
• 47a05
• 47s99