Andrica D., Rassias M.Th. (Eds.) Differential and Integral Inequalities

Springer, 2019. — 848 p. — (Springer Optimization and Its Applications 151). — ISBN: 978-3-030-27406-1.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.Convexity Variants and Fejer Inequalities with General Weight
Error Estimates of Approximations for the Complex Valued Integral Transforms
Convexity Revisited: Methods, Results, and Applications
Some New Methods for Generating Convex Functions
Harmonic Exponential Convex Functions and Inequalities
On the Hardy–Sobolev Inequalities
Two Points Taylor’s Type Representations with Integral Remainders
Some Weighted Inequalities for Riemann–Stieltjes Integral When a Function Is Bounded
Cauchy–Schwarz Inequality and Riccati Equation for Positive Semidefinite Matrices
Inequalities for Solutions of Linear Differential Equations in a Banach Space and Integro–Differential Equations
Best Constants for Poincaré–Type Inequalities in Wn1(0,1)
Best Constants for Weighted Poincaré–Type Inequalities
Operator Inequalities Involved Wiener–Hopf Problems in the Open Unit Disk
Some New Hermite–Hadamard Type Integral Inequalities via Caputo k–Fractional Derivatives and Their Applications
Some New Hermite–Hadamard Type Integral Inequalities for Twice Differentiable Mappings and Their Applications
Inequalities in Statistics and Information Measures
Multiple Hardy–Littlewood Integral Operator Norm Inequalities
Norm Inequalities for Generalized Fractional Integral Operators
Application of Davies–Petersen Lemma
Double–Sided Taylor’s Approximations and Their Applications in Theory of Analytic Inequalities
The Levin–Stečkin Inequality and Simple Quadrature Rules
Preview (p, q)–Laplacian Equations with Convection Term and an Intrinsic Operator
Iterative Methods for Variational Inequalities
Recent Developments of Lyapunov–Type Inequalities for Fractional Differential Equations
Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study
Exact Bounds on the Zeros of Solutions of Second–Order Differential Inequalities
Variational Methods for Emerging Real–Life and Environmental Conservation Problems
Meir–Keeler Sequential Contractions and Applications
An Extended Multidimensional Half-Discrete Hardy–Hilbert-Type Inequality with a General Homogeneous Kernel