DISCRETE POINCARE-TYPE INEQUALITIES

Article Sidebar

PDF
Published: Jun 1, 1998
DOI: https://doi.org/10.5556/j.tkjm.29.1998.4287
Keywords:
Poincare-type inequalities

Main Article Content

WING-SUM CHEUNG
Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong.

Abstract




In this paper some discrete analogue of Poincare-type integral inequalities involving many independent variables are established. These in turn can be used to serve as generators of other interesting discrete inequalities.




Article Details

How to Cite
CHEUNG, W.-S. (1998). DISCRETE POINCARE-TYPE INEQUALITIES. Tamkang Journal of Mathematics, 29(2), 145–153. https://doi.org/10.5556/j.tkjm.29.1998.4287
Issue
Vol. 29 No. 2 (1998)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, New York, 1965

W. S. Cheung, "On integral inequalities of the Sobolev type," Aequationes Math. 49(1995), 153-159.

W . S. Cheung, "On Poincare type integral inequalities," Proc. Amer . Math. Soc. 119, No.3 (1993), 857-863.

W. S. Cheung, "Some multi-dimensional integral inequalities," to appear.

G. H. Hardy, J. E. Littlewood and G. P6lya, Inequalities, Cambridge Univ. Press, Cam­bridge, 1952.

C. O. Horgan, "Integral bounds for solutions of nonlinear reaction-diffusion equations," J. Appl. Math. Phys. (ZAMP) 28(1977), 197-204.

C. O. Horgan and R. R. Nachlinger, "On the domain of attraction for steady states in heat conduction," Internat. J. Engrg. Sci. 14(1976), 143-148

C. O. Horgan and L. T. Wheeler, "Spatial decay estimates for the Navier-Stokes equations with applications to the problem of entry flow," SIAM J. Appl. Math. 35(1978), 97-116.

G. V. Milovanovic, D. S. Mitrinovic and Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific Puhl. Co., 1994.

D. S. Mitrinovic, Analytic inequalities, Springer-Verlag, Berlin, 1970.

L. Nirenberg, "On elliptic partial differential equations," Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)13(1959), 116-162.

B. G. Pachpatte, "On Poincare-type integral inequalities," J. Math. Anal. Appl. 114(1986), 111- 115.

B. G. Pachpatte, "On some new integral inequalities in several independent variables," Chinese J. Math. 14(1986), 69-79.

Th. M. Rassias, "On certain properties of eigenvalues and the Poincare inequality", Global Analysis-Analysis on Manifolds, Teubner-Texte zur Math, Teubner Leipzig, Band 57(1983), 282-300.

Th. M. Rassias, "Un contre-exemple al'inegalite de.Poincare," C. R. Acad. Sciences Paris, 284(1977), 409-412.