Mean Convergence of Grünwald Interpolation Operators

Convergence of Integro Quartic and Sextic B-Spline interpolation

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

Nonlinear Positive Interpolation Operators for Analysis with Multilevel Grids

We introduce some nonlinear positive and negative interpolation operators. The interpolation need to preserve positivity or negativity of a function. In addition, the interpolation must be pointwise below or above the function. Some of the operators also have the pointwise monotone property over refined meshes. It is also desirable that the interpolation have the needed approximation and stabil...

BV-norm convergence of interpolation approximations for Frobenius-Perron operators

Strong convergence theorem for finite family of m-accretive operators in Banach spaces

The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

Interpolation, Maximal Operators, and the Hilbert Transform

Real-variable methods are used to prove the Marcinkiewicz Interpolation Theorem, boundedness of the dyadic and Hardy-Littlewood maximal operators, and the Calderón-Zygmund Covering Lemma. The Hilbert transform is defined, and its boundedness is investigated. All results lead to a final theorem on the pointwise convergence of the truncated Hilbert transform