LEADER 05447nam 22007575 450 001 9910799219103321 005 20251127170401.0 010 $a9783031464874 010 $a3031464877 024 7 $a10.1007/978-3-031-46487-4 035 $a(CKB)29526804400041 035 $a(MiAaPQ)EBC31071223 035 $a(Au-PeEL)EBL31071223 035 $a(DE-He213)978-3-031-46487-4 035 $a(OCoLC)1417759539 035 $a(EXLCZ)9929526804400041 100 $a20240104d2023 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExploring Mathematical Analysis, Approximation Theory, and Optimization $e270 Years Since A.-M. Legendre?s Birth /$fedited by Nicholas J. Daras, Michael Th. Rassias, Nikolaos B. Zographopoulos 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (474 pages) 225 1 $aSpringer Optimization and Its Applications,$x1931-6836 ;$v207 311 08$a9783031464867 327 $aPreface -- On a version of Jensen-Steffensen inequality and a note on inequalities in several variables -- A class of dynamic unilateral contact problems with sub-differential friction law -- Square-free values of $[\textrm{n}^c \tan^\theta(\log \textrm{n})]$ -- Ostrowski and Trapezoid Type Inequalities for Riemann-Liouville Fractional Integrals of Functions with Bounded Variation -- A strong maximum principle for general nonlinear operators -- On the Application of Ergodic Theory to an Alternating Series Expansion for Real Numbers -- Bounds for Similarity Condition Numbers of Unbounded Operators -- Legendre's Geometry and Trigonometry at the Evelpides School (Central Military School) during the Kapodristrian period -- The Overshadowing of Euclid?s Geometry by Legendre?s Géométrie in the Modern Greek Education -- Finite Element Methods with Higher Order Polynomials -- On Local Asymptotics for Orthonormal Polynomials -- New Trends inGeometric Function Theory -- A unified approach to extended general quasi variational inclusions -- On a Reverse Hilbert-Type Inequality in the Whole Plane with Multi-Parameters -- Generating functions for the Fubini type polynomials and their applications -- Kleene Fixed Point Theorems and Applications -- On ergodic states, spontaneous symmetry breaking and quasi-averages -- Improvement of the Hardy inequality and Legendre polynomials. 330 $aThis book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy?s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume. 410 0$aSpringer Optimization and Its Applications,$x1931-6836 ;$v207 606 $aFunctions of real variables 606 $aMathematical optimization 606 $aApproximation theory 606 $aFunctional analysis 606 $aOperator theory 606 $aNumber theory 606 $aReal Functions 606 $aOptimization 606 $aApproximations and Expansions 606 $aFunctional Analysis 606 $aOperator Theory 606 $aNumber Theory 615 0$aFunctions of real variables. 615 0$aMathematical optimization. 615 0$aApproximation theory. 615 0$aFunctional analysis. 615 0$aOperator theory. 615 0$aNumber theory. 615 14$aReal Functions. 615 24$aOptimization. 615 24$aApproximations and Expansions. 615 24$aFunctional Analysis. 615 24$aOperator Theory. 615 24$aNumber Theory. 676 $a515.8 700 $aDaras$b Nicholas J$01586312 701 $aRassias$b Michael Th$0993670 701 $aZographopoulos$b Nikolaos B$01586313 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910799219103321 996 $aExploring Mathematical Analysis, Approximation Theory, and Optimization$93872649 997 $aUNINA