George A. Anastassiou & John Michael Rassias 
Frontiers in Functional Equations and Analytic Inequalities 

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: 

• Hyperstability of a linear functional equation on restricted domains


• Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations


• Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations


• General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces


• Stabilities of Functional Equations via Fixed Point Technique


• Measure zero stability problem for the Drygas functional equation with complex involution


• Fourier Transforms and Ulam Stabilities of Linear Differential Equations


• Hyers–Ulam stability of a discrete diamond–alpha derivative equation


• Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. 
  

The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy,  Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book’s results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interestingadvanced seminars can be given out of this book. 

Содержание

Complex Korovkin Theory via inequalities, a quantitative approach.- Hyperstability of a lineat functional Equation aon restricted domains.- ‘Hyers-Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations’.-  ‘Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations’.- On a variant of  -Wilson’s functional equation with an endomorphism.- On the additivity of maps preserving triple Jordan product A B +  B A on algebras.- ‘General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces’.- ‘Stabilities of MIQD and MIQA Functional Equations via Fixed Point Technique’.- Hyers-Ulam Stability of First Order Differential Equation via Integral Inequality.- ‘Stability of a n-Dimensional Functional Equation in Banach Space and Fuzzy Normed Space’.- Measure zero stability problem for Drygas functional equation with complex involution.- Fourier Transforms and Ulam Stabilities of Linear Di erential Equations.- A class of functional equations of type d’Alembert on monoids.- Hyers–Ulam stability of a discrete diamond–alpha derivative equation.- Hyers–Ulam stability for a first-order linear proportional nabla difference operator.- Solution of generalized Jensen and quadratic functional equation.- On some functional equations with applications in Networks.- Approximate solutions of an (AQQ) additive-quadratic-quartic functional equation.- Ostrowski type inequalities involving sublinear integrals.- ‘Inequalities for special strong differential superordinations using a generalized S˘al˘agean operator and Ruscheweyh derivative’.- Conformable fractional inequalities.- New inequalities for h-quasiconvex functions.- Local fractional Inequalities.- ‘Some new Hermite-Hadamard type integral inequalities for twice differentiable generalized ¹¹h1; h2º; ¹ 1;  2ºº-convex mappings and their applications’.- Hardy’s Type Inequalities Via Conformable Calculus.- Inequalities for Symmetrized or Anti-symmetrized Inner Products of Complex-Valued Functions Defined on an Interval.- Generalized Finite Hilbert Transform and Some Basic Inequalities.- Inequalities of Hermite-Hadamard Type for Composite Convex Functions.- Error Estimation for Approximate Solutions of Delay Volterra Integral Equations.- Harmonic and Trace Inequalities in Lipschitz Domains.- Dirichlet Beta Function via Generalized Mathieu Series Family.- Recent research on Levinson’s inequality.- Integral Norm Inequalities for Various Operators on Differential Forms.- Hadamard integral inequality for the class of harmonically (; )-convex functions.- Norm Inequalities for Singular Integrals Related to Operators and Dirac-Harmonic Equations.- Inequalities for analytic functions defined by a fractional integral operator.

Об авторе

George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including ‘Fractional Differentiation Inequalities’ (c) 2009, ‘Fuzzy Mathematics: Approximation Theory’ (c) 2010, ‘Intelligent Systems: Approximation by Artificial Neural Networks’ (c) 2014, ‘The History of Approximation Theory’ (c) 2005, ‘Modern Differential Geometry in Gauge Theories’ (c) 2006, and more.




John Michael Rassias is a Ph.D. graduate of the University of California, Berkeley. He is currently  Emeritus Professor of the National and Kapodistrian University of Athens, Greece. Professor John M. Rassias  is a leading mathematician and researcher in Mathematics. He has published academic papers in the following research areas: Functional Equations and Inequalities (more than 300 papers) in peer-reviewed leading scientific journals. Partial Differential Equations (more than 100 papers). He has also published 36  books and monographs in  Mathematics.