the aim of this paper is to study the behaviour of certain sequence of nonlinear durrmeyer operators $nd_{n}f$ of the form $$(nd_{n}f)(x)=intlimits_{0}^{1}k_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{n}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% k_{n}left( x,t,uright) $ satisfies some suitable assumptions. here we estimate the rate...

Abstract— We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely de£ned and...

The terminology and notation used here are introduced in the following articles: [18], [8], [20], [5], [7], [6], [3], [1], [17], [13], [19], [14], [2], [4], [15], [10], [11], [9], and [12]. One can prove the following propositions: (1) Let X, Y , Z be complex linear spaces, f be a linear operator from X into Y , and g be a linear operator from Y into Z. Then g · f is a linear operator from X in...

Let X be a set, let Y be a non empty set, let F be a function from [: C, Y :] into Y , let c be a complex number, and let f be a function from X into Y . Then F ◦(c, f) is an element of Y X . We now state the proposition (1) Let X be a non empty set and Y be a complex linear space. Then there exists a function M1 from [: C, (the carrier of Y ) X :] into (the carrier of Y ) such that for every C...