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Displaying 101 –
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313
2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36,
42A10.The paper presents a method of relating two K-functionals by
means of a continuous linear transform of the function. In particular, a
characterization of various weighted K-functionals by unweighted fixed-step
moduli of smoothness is derived. This is applied in estimating the rate of
convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia
University....
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains , . We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in , comprising the countably-normed spaces of I. M. Babuška and B. Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial high...
2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.In this paper, we obtain some statistical Korovkin-type approximation theorems including fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.
2000 Mathematics Subject Classification: 41A25, 41A36.In the present paper, we improve the classical trigonometric Korovkin theory by using the concept of statistical convergence from the summability theory and also by considering the fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.
In the present paper, we prove a global direct theorem for the modified Baskakov type operators in terms of so called Ditzian-Totik modulus of smoothness.
We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high...
In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.
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