Analyzing the linearity of some operators

Linear operators occupy an important place in functional analysis and linear algebra, which are among the most important and substantive disciplines of mathematics, whose methods and results have created an indispensable apparatus for the development of numerical mathematics, theory of approximations, equations differential and especially mathematical physics and applied mathematics. Also, linear operators are a central object of study in vector space theory. A linear operator is a function which satisfies the conditions of additivity and homogeneity. Not every function is linear operators. We will try to explore some functions which are also linear operators