Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-26T22:26:36.659Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain mapping properties of rational complex planar splines

Published online by Cambridge University Press:  24 October 2008

H. P. Dikshit ,
A. Ojha  and
A. Sharma
H. P. Dikshit
Affiliation:
R. D. University, Jabalpur, India
A. Ojha
Affiliation:
R. D. University, Jabalpur, India
A. Sharma
Affiliation:
University of Alberta, Edmonton, Canada
Get access Rights & Permissions [Opens in a new window]

Summary

Considering a certain partition of a given compact region in the complex plane, interpolatory, convergence and quasiconformal properties of interpolants from the class of continuous piecewise functions with pieces as quadratic polynomials in z and were studied recently in [3] and [7]. In the present paper we succeed in showing that the foregoing mapping properties continue to hold for interpolants from a certain class of continuous piecewise rational polynomial functions in z and

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 141 - 149
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Ahlfors., L. V.Lectures on Quasiconformal Mappings. Van Nostrand Mathematical Studies, vol. 10 (1966).Google Scholar
[2]Ciarlet, P. G. and Raviart., P. A.General Lagrange and Hermite interpolation in ℝn with applications to finite element methods. Arch. Rational Mech. Anal. 46 (1972), 177–199.CrossRefGoogle Scholar
[3]Dikshit, H. P. and Ojha., A.On convergence and quasiconformality of complex planar spline interpolants. Math. Proc. Cambridge Philos. Soc. 99 (1986), 347–356.Google Scholar
[4]Lehto, O. and Virtanen., K. I.Quasikonforme Abbildungen (Springer-Verlag, 1972).Google Scholar
[5]Martio, O., Rickman, S.and J. Väisälä. Definitions for quasiregular mappings. Ann. Acad. Sci. Fenn. Ser. AI Math. 448 (1969).Google Scholar
[6]Opfer, G. and Puri., M. L.Complex planar splines. J. Approx. Theory 31 (1981), 382–402.Google Scholar
[7]Opfer, G. and Schober., G.On convergence and quasiregularity of interpolating complex planar splines. Math. Z. 180 (1982), 469–481.CrossRefGoogle Scholar
[8]Wachspress., E. L.A Rational Finite Element Basis (Academic Press, 1975).Google Scholar