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Rate of convergence of Szász-beta operators based on q-integers

100%

Gupta P. , Agrawal P. N.

2017

tom Vol. 50, nr 1

130--143

The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

Existence of periodic solutions for quasilinear ordinary differential eqasilinear ordinary diefferential equations with discontinuities

84%

Matzakos N. , Papageorgiou N.

tom Vol. 33, nr 4

753-770

We consider a quasilinear differential equation with discontinuous right hand side and periodic boundary conditions. To obtain an existence theory we pass to a relevant multivalued variant of the original problem, which we solve. Our approach is a mixture of the variational method (for nonsmooth locally Lipschitz functionals) and of the method of upper and Iower solutions. The mixing of these two techniques is made possible by a nonresonance condition below the first nonzero eigenvalue of the one-dimensional p-Laplacian with periodic boundary conditions.