A class of Lagrange-Newton-SQP methods is investigated for optimal control problems governed by semilinear parabolic initial-boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order suucient optimality condition for the reference solu...

We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes qintegers.We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section 3, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-ty...

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, t...

We prove a constructive version of the Schwarz reflection principle. Our proof techniques are in line with Bishop’s development of constructive analysis. The principle we prove enables us to reflect analytic functions in the real line, given that the imaginary part of the function converges to zero near the real line in a uniform fashion. This form of convergence to zero is classically equivale...

We consider probability measure estimation in a nonparametric model using a leastsquares approach under the Prohorov metric framework. We summarize the computational methods and their convergence results that were developed by our group over the past two decades. New results are presented on the bias and the variance due to the approximation and the pointwise asymptotic normality of the approxi...

The paper describes the structure of a linear continuous operator on space functions in topology pointwise convergence. corresponding theorem is generalization A.V.Arkhangel'skii's general form functional such spaces.

We investigate the pointwise convergence of solution to fractional Schrödinger equation in $\mathbb{R}^2$. By establishing $H^s(\mathbb{R}^2) - L^3(\mathbb{R}^2)$ estimates for associated maximal operator provided that $s > 1/3$, we improve previous result obtained by Miao, Yang, and Zheng [19]. Our extend refined Strichartz Du, Guth, Li [10] a general class elliptic functions.