Analytic and Geometric Inequalities and Applications

ISBN-13: 9789401059381 / Angielski / Miękka / 2012 / 377 str.

Themistocles RASSIAS;Hari M. Srivastava

Opis

This volume is devoted to recent advances in a variety of inequalities in mathematical analysis and geometry. Subjects dealt with include: differential and integral inequalities; fractional order inequalities of Hardy type; multi-dimensional integral inequalities; Gruss' inequality; Laguerre-Samuelson inequality; Opial type inequalities; Furuta inequality; distortion inequalities; problem of infimum in the positive cone; external problems for polynomials; Chebyshev polynomials; bounds for the zeros of polynomials; open problems on eigenvalues of the Laplacian; obstacle boundary value problems; bounds on entropy measures for mixed populations; connections between the theory of univalent functions and the theory of special functions; and degree of convergence for a class of linear operators. A wealth of applications of the above is also included. Audience: This book will be of interest to mathematicians whose work involves real functions, functions of a complex variable, special functions, integral transforms, operational calculus, or functional analysis."

Spis treści

Preface. Problem of Infimum in the Positive Cone; T. Ando. Open Problems on Eigenvalues of the Laplacian; M.S. Ashbaugh. On an Inequality of S. Bernstein and the Gauss-Lucas theorem; A. Aziz, N.A. Rather. Second Order Opial Inequalities in LP spaces and Applications; R. Brown, et al. On Multi-dimensional Integral Inequalities and Applications; W.-S. Cheung, T.M. Rassias. Some Inequalities for Triangle: Old and New Results; R.Z. Djordjevic. A Treatise on Grüss' Inequality; A.M. Fink. A>=B>=0 Ensures (B r/2 ApB r/2)1/q>=(B r/2£/XX£pB r/2)1/q for r>=o, p>=o, q>=1 with (1+r)q>=p+r and its Recent Applications; T. Furuta. Degree of Convergence for a Class of Linear Operators; N.K. Govil, R.N. Mohapatra. Some Comments and a Bibliography on the Laguerre-Samuelson Inequality With Extensions and Applications in Statistics and Matrix Theory; S.T. Jensen, G.P.H. Styan. Fractional Order Inequalities of Hardy Type; A. Kufner. Theory of Differential and Integral Inequalities with Initial Time Difference and Applications; V. Lakshmikantham, A.S. Vatsala. Numerical Radii of Some Companion Matrices and Bounds for the Zeros of Polynomials; H. Linden. Bounds on Entropy Measures for Mixed Populations; M. Matic, et al. Extremal Problems and Inequalities of Markov-Bernstein Type for Polynomials; G.V. Milovanovic. On Alpha-quasi-convex Functions Defined by Convolution with Incomplete Beta Functions; K.I. Noor. Fourth Order Obstacle Boundary Value Problems; M.A. Noor, E.A. Al-Said. On Some Generalized Opial Type Inequalities; B.G. Pachpatte. Controlling the Velocity of Brownian Motion by its Terminal Value; G. Peskir. Chebyshev Polynomials with IntegerCoefficients; I.E. Pritsker. Distortion Inequalities for Analytic and Univalent Functions Associated with Certain Fractional Calculus and Other Linear Operators; H.M. Srivastava.