Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy-Hadamard, Chebychev, Markov, Euler's constant, Grothendieck, Hilbert, Hardy, Carleman, Landau-Kolmogorov, Carlson, Bernstein-Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.

Autorentext
Dorin Andrica is a professor of mathematics at Babe-Bolyai University in Cluj Napoca, Romania. His interests include Critical Point Theory and Applications, Nonlinear Analysis, Approximation Theory, Number Theory. Other than his several research publications, Prof. Andrica has published extensively with Springer on an array of topics. Being a master of Olympiad caliber problems, he has couched several teams for the Mathematical Olympiads and has published popular books in this subject.

Themistocles M. Rassias is a professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Prof. Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Prof. Rassias has published as author or editor many books and volumes with Springer. In addition to having received several awards, Themistocles M. Rassias' work has received a large number of citations.

Inhalt
Convexity variants and Fejer inequalities with general weight.- Error estimates of approximations for the complex valued integral transforms (Abramovich).- Some New Methods for Generating Convex Functions (Agli Aljinovi).- Convexity Revisited: Methods, Results, and Applications (Andrica).- Harmonic exponential convex functions and inequalities (Uzair Awan).- On the Hardy-Sobolev inequalities (Cotsiolis).- Two points taylor’s type representations with integral remainders (Dragomir).- Some weighted inequalities for Riemann-Stieltjes integral when a function is bounded (Dragomir).- Cauchy-Schwarz inequality and Riccati equation for positive semide nite matrices (Fujii).- "Inequalities for Solutions of Linear Differential Equations in a Banach Space and Integro-Differential Equations" (Gil).- Best Constants for Poincar´e-Type Inequalities in Wn1 (0;1) (Guessab).- Best Constants for Weighted Poincar´e-Type Inequalities (Guessab).- Operator inequalities involvedWiener-Hopf problems in the open unit disk (Ibrahim).- Some new Hermite-Hadamard type integral inequalities via Caputo k-fractional derivatives and their applications (Kashuri).- Some new Hermite-Hadamard type integral inequalities for twice differentiable mappings and their applications (Kashuri).- Inequalities in Statistics and Information Measures (Kitsos).- Multiple Hardy-Littlewood Integral Operator Norm Inequalities (Jichang).- Norm Inequalities for Generalized Fractional Integral Operators (Jichang).- Application of Davies-Petersen Lemma (Kumar).- Double-sided Taylor's approximations and their applications in Theory of analytic inequalities (Maleevi´c).- The Levin-Steckin Inequality and Simple Quadrature Rules (Mercer).- (p;q)-Laplacian equations with convection term and an intrinsic operator (Motreanu).- Iterative methods for variational inequalities (Aslam Noor).- Recent developments of Lyapunov-type inequalities for fractional differential equations (Ntouyas).- Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study (Obaiys).- Exact bounds on the zeros of solutions of second-order differential inequalities (Pinelis).- Variational methods for emerging real-life and environmental conservation problems (Scrimali).- Meir-Keeler sequential contractions and applications ( Turinici).- An Extended Multidimensional Half-Discrete Hardy-Hilbert-Type Inequality with a General Homogeneous Kernel (Yang).