By Tsuyoshi Ando (auth.), Themistocles M. Rassias, Hari M. Srivastava (eds.)

ISBN-10: 9401059381

ISBN-13: 9789401059381

ISBN-10: 9401145776

ISBN-13: 9789401145770

Analytic and Geometric Inequalities and functions is dedicated to fresh advances in various inequalities of Mathematical research and Geo metry. matters handled during this quantity contain: Fractional order inequalities of Hardy kind, differential and indispensable inequalities with preliminary time vary ence, multi-dimensional crucial inequalities, Opial style inequalities, Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality with extensions and functions in records and matrix conception, distortion inequalities for ana lytic and univalent capabilities linked to yes fractional calculus and different linear operators, challenge of infimum within the optimistic cone, alpha-quasi convex services outlined through convolution with incomplete beta services, Chebyshev polynomials with integer coefficients, extremal difficulties for poly nomials, Bernstein's inequality and Gauss-Lucas theorem, numerical radii of a few significant other matrices and limits for the zeros of polynomials, measure of convergence for a category of linear operators, open difficulties on eigenvalues of the Laplacian, fourth order main issue boundary worth difficulties, bounds on entropy measures for combined populations in addition to controlling the rate of Brownian movement via its terminal price. A wealth of functions of the above can also be incorporated. we want to exhibit our appreciation to the prestigious mathematicians who contributed to this quantity. eventually, it truly is our excitement to recognize the high quality cooperation and guidance supplied via the employees of Kluwer educational Publishers. June 1999 Themistocles M. Rassias Hari M.

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3. 4. 5. 6. 7. 8. 9. S. D. Benguria, Proof of the Payne-P6lyaWeinberger conjecture, Bull. Amer. Math. Soc. 25 (1991), 19-29. S. D. Benguria, A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions, Annals of Mathematics 135 (1992), 601-628. S. D. Benguria, Isoperimetric bound for A3/A2 for the membrane problem, Duke Math. J. 63 (1991), 333-341. S. D. Benguria, Isoperimetric bounds for higher eigenvalue ratios for the n-dimensional fixed membrane problem, Proc.

54, part 1, R. -T. Yau, editors, Amer- 28 ican Mathematical Society, Providence, Rhode Island, 1993, pp. 1-28 [reprinted as pp. 365-409 of [40]]. ON AN INEQUALITY OF S. BERNSTEIN AND THE GAUSSLUCAS THEOREM A. A. RATHER Post-Graduate Department of Mathematics and Statistics University of Kashmir Hazratbal, Srinagar 19006 India Abstract. In this paper we first present an interesting generalization of the Gauss-Lucas Theorem. Next we use this result as a basic tool to prove certain compact generalizations of the well-lmown inequalities of S.

M. M. ), Analytic and Geometric Inequalities and Applications, 53-67. © 1999 Kluwer Academic Publishers. 54 all share the same spirit as Poincare's inequality does. In general, such variations of Poincare's inequality are collectively known as Poincare-type integral inequalities. A brief account of such inequalities can be found in, say, Beckenbach-Bellman [1], Hardy-Littlewood-P6Iya [11], Mitrinovic [17], Nirenberg [18], and more recently Horgan et al [13, 14, 15], Milovanovic-Mitrinovic-Rassias [16], Pachpatte [19, 21], Rassias [24, 25], and Cheung [3, 6, 7].

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