𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Three Conjectures on Shepard Interpolatory Operators

✍ Scribed by Tingfan Xie; Ren Jiang Zhang; Songping Zhou

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
228 KB
Volume
93
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

After establishing direct and converse approximation theorems for the Shepard interpolatory operators, J. Szabados (Approx. Theory Appl. 7, No. 3, 1991, 63 76) left some open saturation problems (``the most intriguing questions'' as he said), which he raised as three conjectures. The present paper proves the second parts of some conjectures, but constructs counterexamples to show that the first parts of three conjectures are not true. The constructive procedure uses some novel ideas and techniques.

πŸ“œ SIMILAR VOLUMES

BalΓ‘zs–Shepard Operators on Infinite Int
BalΓ‘zs–Shepard Operators on Infinite Intervals, II
✍ G Mastroianni; J Szabados πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 248 KB

The weighted uniform convergence of the Bala zs Shepard operator is considered on the real line. As a consequence of the main result, it is proved that for a wide class of weights, rational functions are always dense in the space of continuous functions, in contrast to the polynomials where the Akhi

On a conjecture for an overdetermined pr
On a conjecture for an overdetermined problem for the biharmonic operator
✍ V. Goyal; P.W. Schaefer πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 146 KB

It has been proven that if the solution exists to an inhomogeneous biharmonic equation in the plane where the values of the solution, the normal derivative of the solution, and the Laplacian of the solution are prescribed on the boundary, then the domain is a disk. This result has been extended to N