04113nam 2200601 a 450 991078855650332120230725045538.01-283-14489-19786613144898981-4317-63-2(CKB)3360000000001401(EBL)731227(OCoLC)741492827(SSID)ssj0000631674(PQKBManifestationID)12234343(PQKBTitleCode)TC0000631674(PQKBWorkID)10592224(PQKB)10058126(MiAaPQ)EBC731227(WSP)00001190 (Au-PeEL)EBL731227(CaPaEBR)ebr10479811(CaONFJC)MIL314489(EXLCZ)99336000000000140120110712d2011 uy 0engurbn|||||||||txtccrAdvanced inequalities[electronic resource] /George A. AnastassiouSingapore ;Hackensack, N.J. World Scientific Pub. Co.20111 online resource (450 p.)Series on concrete and applicable mathematics,1793-1142 ;v. 11Description based upon print version of record.981-4317-62-4 Includes bibliographical references and index.Preface; Contents; 1. Introduction; 2. Advanced Univariate Ostrowski Type Inequalities; 3. Higher Order Ostrowski Inequalities; 4. Multidimensional Euler Identity and Optimal Multidimensional Ostrowski Inequalities; 5. More on Multidimensional Ostrowski Type Inequalities; 6. Ostrowski Inequalities on Euclidean Domains; 7. High Order Ostrowski Inequalities on Euclidean Domains; 8. Ostrowski Inequalities on Spherical Shells; 9. Ostrowski Inequalities on Balls and Shells Via Taylor{Widder Formula; 10. Multivariate Opial Type Inequalities for Functions Vanishing at an Interior Point11. General Multivariate Weighted Opial Inequalities 12. Opial Inequalities for Widder Derivatives; 13. Opial Inequalities for Linear Differential Operators; 14. Opial Inequalities for Vector Valued Functions; 15. Opial Inequalities for Semigroups; 16. Opial Inequalities for Cosine and Sine Operator Functions; 17. Poincare Like Inequalities for Linear Differential Operators; 18. Poincare and Sobolev Like Inequalities for Widder Derivatives; 19. Poincare and Sobolev Like Inequalities for Vector Valued Functions; 20. Poincare Type Inequalities for Semigroups, Cosine and Sine Operator Functions21. Hardy-Opial Type Inequalities 22. A Basic Sharp Integral Inequality; 23. Estimates of the Remainder in Taylor's Formula; 24. The Distributional Taylor Formula; 25. Chebyshev-Gruss Type Inequalities Using Euler Type and Fink Identities; 26. Gruss Type Multivariate Integral Inequalities; 27. Chebyshev-Gruss Type Inequalities on Spherical Shells and Balls; 28. Multivariate Chebyshev-Gruss and Comparison of Integral Means Inequalities; 29. Multivariate Fink Type Identity Applied to Multivariate Inequalities; Bibliography; List of Symbols; IndexThis monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end. The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities are examSeries on concrete and applicable mathematics ;v. 11.Inequalities (Mathematics)Inequalities (Mathematics)515.26Anastassiou George A60024MiAaPQMiAaPQMiAaPQBOOK9910788556503321Advanced inequalities3676445UNINA