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...

For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence.  We study a functional characterization of the covering property of Hurewicz.

We now discuss convergence of the Fourier series on compact intervals I. ‘Convergence’ depends on the notion of convergence we use, such as (i) L: uj → u in L if ‖uj − u‖L2 → 0 as j →∞. (ii) uniform, or C: uj → u uniformly if ‖uj−u‖C0 = supx∈I |uj(x)−u(x)| → 0. (iii) uniform with all derivatives, or C∞: uj → u in C∞ if for all non-negative integers k, supx∈I |∂uj(x)− ∂u(x)| → 0. (iv) pointwise:...