Differential and Integral Inequalities

Description

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. Front Matter ....Pages i-ix Convexity Variants and Fejer Inequalities with General Weight (Shoshana Abramovich)....Pages 1-19 Error Estimates of Approximations for the Complex Valued Integral Transforms (Andrea Aglić Aljinović)....Pages 21-47 Convexity Revisited: Methods, Results, and Applications (Dorin Andrica, Sorin Rădulescu, Marius Rădulescu)....Pages 49-134 Some New Methods for Generating Convex Functions (Dorin Andrica, Sorin Rădulescu, Marius Rădulescu)....Pages 135-229 Harmonic Exponential Convex Functions and Inequalities (Muhammad Uzair Awan, Muhammad Aslam Noor, Khalida Inayat Noor)....Pages 231-264 On the Hardy–Sobolev Inequalities (Athanase Cotsiolis, Nikos Labropoulos)....Pages 265-287 Two Points Taylor’s Type Representations with Integral Remainders (Silvestru Sever Dragomir)....Pages 289-309 Some Weighted Inequalities for Riemann–Stieltjes Integral When a Function Is Bounded (Silvestru Sever Dragomir)....Pages 311-339 Cauchy–Schwarz Inequality and Riccati Equation for Positive Semidefinite Matrices (Masatoshi Fujii)....Pages 341-350 Inequalities for Solutions of Linear Differential Equations in a Banach Space and Integro–Differential Equations (Michael Gil’)....Pages 351-390 Best Constants for Poincaré–Type Inequalities in \(W^{n}_1(0,1)\) (Allal Guessab, Gradimir V. Milovanović)....Pages 391-402 Best Constants for Weighted Poincaré–Type Inequalities (Alla Guessab)....Pages 403-421 Operator Inequalities Involved Wiener–Hopf Problems in the Open Unit Disk (Rabha W. Ibrahim)....Pages 423-433 Some New Hermite–Hadamard Type Integral Inequalities via Caputo k–Fractional Derivatives and Their Applications (Artion Kashuri, Rozana Liko)....Pages 435-458 Some New Hermite–Hadamard Type Integral Inequalities for Twice Differentiable Mappings and Their Applications (Artion Kashuri, Rozana Liko)....Pages 459-479 Inequalities in Statistics and Information Measures (Christos P. Kitsos, Thomas L. Toulias)....Pages 481-508 Multiple Hardy–Littlewood Integral Operator Norm Inequalities (J. C. Kuang)....Pages 509-533 Norm Inequalities for Generalized Fractional Integral Operators (J. C. Kuang)....Pages 535-548 Application of Davies–Petersen Lemma (Manish Kumar, R. N. Mohapatra)....Pages 549-568 Double–Sided Taylor’s Approximations and Their Applications in Theory of Analytic Inequalities (Branko Malešević, Marija Rašajski, Tatjana Lutovac)....Pages 569-582 The Levin–Stečkin Inequality and Simple Quadrature Rules (Peter R. Mercer)....Pages 583-588 (p, q)–Laplacian Equations with Convection Term and an Intrinsic Operator (Dumitru Motreanu, Viorica Venera Motreanu)....Pages 589-601 Iterative Methods for Variational Inequalities (Muhammad Aslam Noor, Khalida Inayat Noor, Themistocles M. Rassias)....Pages 603-618 Recent Developments of Lyapunov–Type Inequalities for Fractional Differential Equations (Sotiris K. Ntouyas, Bashir Ahmad, Theodoros P. Horikis)....Pages 619-686 Hypersingular Integrals in Integral Equations and Inequalities: Fundamental Review Study (Suzan J. Obaiys, Rabha W. Ibrahim, Ahmad F. Ahmad)....Pages 687-717 Exact Bounds on the Zeros of Solutions of Second–Order Differential Inequalities (Iosif Pinelis)....Pages 719-724 Variational Methods for Emerging Real–Life and Environmental Conservation Problems (Laura Scrimali, Antonino Maugeri)....Pages 725-759 Meir–Keeler Sequential Contractions and Applications (Mihai Turinici)....Pages 761-829 An Extended Multidimensional Half-Discrete Hardy–Hilbert-Type Inequality with a General Homogeneous Kernel (Bicheng Yang)....Pages 831-854