ABSTRACTS OF TALKS (the information in brackets refers to session numbers) On Simultaneous Approximation in Function Spaces [C-5B]

S OF TALKS (the information in brackets refers to session numbers) On Simultaneous Approximation in Function Spaces [C-5B] E. Abu-Sirhan Tafila Technical University, Tafila, Jordan [email protected] The problem of simultaneous approximation in function spaces has attracted many researcher recently. Major results on the space of vector valued continuos functions started to appear early nineties. In 2002, results on simultaneous approximation in p-Bochner integrable functions were published. The object of this paper is to give a charactarization for the subspaces of Bochner integrable functions space to be simultaneously proximinal. Lipschitz Constant for Vector Valued Approximation [C-5B] Mohammad A. AlQudah* and James R. Angelos Central Michigan University, Mount Pleasant, MI, USA [email protected] We present a formula for the local Lipschitz constant for uniform approximation of f on a discrete subset X of [−1, 1] from a generalized Haar subspace of dimension n, under the restriction thatX has exactly (m+1) points, where m is the dimension of the component spaces comprising the generalized Haar subspace G. Numerical Methods for Fully Nonlinear Equations [M-13B] Gerard Awanou Northern Illinois University [email protected] While the theory of second order fully nonlinear equations has received considerable attention, there is a paucity of numerical methods, especially finite element methods, for these equations. As it is not in general possible to weaken the order of the equations through integration by parts, spaces of C spline functions form an appropriate framework to approximate the solution of these equations. We introduce a general framework for numerical solution of these equations and illustrate the performance of the approach with numerical experiments using the spline element method. We treat the examples of the Monge-Ampère and Pucci equations and discuss the convergence of our algorithms. Sharp Inequalities of Kolmogorov Type for Hypersingular Integrals and Some Applications [M-1B] Vladislav Babenko Dnepropetrovsk National University, Ukraine [email protected] In this talk we present several new sharp inequalities of Kolmogorov type for hypersingular integrals in univariate and multivariate case.In particular, we present new inequalities for fractional degrees of differential operators of elliptic and parabolic type. In addition, we present some applications of the obtained results. On the Lp-error of Adaptive Interpolation by Splines on Box Partitions [M-6A] Y. Babenko*, T. Leskevich, J.-M. Mirebeau Sam Houston State University, TX, USA [email protected] We will show that lim N→∞ N n 2 ‖f − s(f,N)‖p = Mp n! ∥