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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
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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

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

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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