In all of these theorems the notion of convergence used in (1-1) and (1-2) has essentially been strong convergence. It is the purpose of the present paper to prove analogous theorems for a certain class of notions of convergence, which will include, in the case of Banach spaces of functions with the sup norm, bounded, pointwise convergence, and convergence of bounded sequences which is uniform ...

Aktuğlu and Gezer [1] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. Recently, Kaya and Gönül [11] proved some analogs of the Korovkin approximation theorem via lacunary equistatistical convergence by using test functions 1, x 1+x , y 1+y , ( x 1+x )2+( y 1+y )2....

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We th...

This paper studies the large time behavior of solutions to semi-linear Cauchy problems with quadratic nonlinearity in gradients. The Cauchy problem considered has a general state space and may degenerate on the boundary of the state space. Two types of large time behavior are obtained: i) pointwise convergence of the solution and its gradient; ii) convergence of solutions to associated backward...

This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis, particularly uniform convergence analysis. To overcome this difficulty, we establish the uniform Lipschitz property of optimal spline coefficients in the `∞-norm b...

In this paper we investigate the rate of convergence of the optimal value function of an innnite horizon discounted optimal control problem as the discount rate tends to zero. Using the Integration Theorem for Laplace transformations we provide conditions on averaged functionals along suitable trajectories yielding at most quadratic pointwise convergence. Under appropriate controllability assum...

In this paper, a Godunov scheme on moving meshes, is studied for a kind of timedependent convection-dominated equations with dynamical boundary layers. The rate of convergence in pointwise norm, which is uniform to the small diffusion parameter 2, O(N−1 +τ), is proved, where N is the number of spatial unknowns and τ the mesh size of temporal meshes. This paper is a successful try on the converg...

A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlineari...

Abstract: We define q-analogues of Fourier-Bessel series, by means of complete qorthogonal systems constructed with the third Jackson q-Bessel function. Sufficient conditions for pointwise convergence of these series are obtained, in terms of a general convergence principle valid for other Fourier series on grids defined over numerable sets. The results are illustrated with specific examples of...

In this paper we study the distributed and boundary optimal control of the Stokes equations in presence of pointwise control constraints. The analysis of the problems involve existence results, as well as necessary conditions and optimality systems. A primal-dual active set strategy is studied for the numerical solution of the problems. For the distributed case, global and local convergence res...