On Some Bounds for Cebysev Functional with Applications

Girish Kapoor

Department of Mathematics, Govt. College Arki, Distt. Solan, Himachal Pradesh, India.

*Corresponding Author E-mail: grshkapoor@gmail.com.

ABSTRACT:

A new lower bound for the unweighted Cebysev functional involving two n-tuples of real numbers is developed. Some related bounds for roots of polynomial equation and bounds for eigen values of a square matrix with real spectrum is obtained.

KEYWORDS: Cebysev’s functional, Discrete Korkine type Identity, Eigenvalues of matrix , roots of polynomial equation.

1. INTRODUCTION: For two n-tuples of real numbers, Consider the Cebysev’s functional

4. REFERENCES:

[1] A. M. Fink, A treatise on Gruss inequality, Anlytic and Geometric Inequalities and Applications, T. M. Rassias and H. M. Srivastava, Editors Kluwer, 1999, 93 - 114.

[2] M. Biernacki, H. Pidek and C. Ryll – Nardzewski, Sur une inegalite entre des integrates definies, Ann. Univ. Marae Curie – Sklodowska, A, 4 (1950), 1- 4.

[3] D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic publishers, Dordrecht, 1993.

[4] J. E. Pecaric, F. Prochan, Y. Tong, Convex functions, Partial ordering and Statistical applications, Academic Press, 1992.

[5] S.T. Jensen, The Laguerre samuelson Inequality with extensions and applications in statistics and matrix theory. M.Sc. Thesis, Department of mathematics and statistics, McGill University, Montreal,Canada, 1999.

[6] H.Wolkowicz and P.H.Styan., Bounds for eigenvalues using traces, Linear Algebra and Its

applications,29:471-506,1980.

[7] H.Wolkowicz and P.H.Styan., More bounds for eigenvalues using traces, Linear Algebra and Its

applications,31:1-17,1980.

Received on 24.01.2014 Accepted on 02.02.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 82-85