Functional Equations in Mathematical Analysis (Springer Optimization and Its Applications Book 52)

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences. Front Matter....Pages i-xvii Front Matter....Pages 1-1 Stability Properties of Some Functional Equations....Pages 3-13 Note on Superstability of Mikusiński’s Functional Equation....Pages 15-17 A General Fixed Point Method for the Stability of Cauchy Functional Equation....Pages 19-32 Orthogonality Preserving Property and its Ulam Stability....Pages 33-58 On the Hyers–Ulam Stability of Functional Equations with Respect to Bounded Distributions....Pages 59-78 Stability of Multi-Jensen Mappings in Non-Archimedean Normed Spaces....Pages 79-86 On Stability of the Equation of Homogeneous Functions on Topological Spaces....Pages 87-96 Hyers–Ulam Stability of the Quadratic Functional Equation....Pages 97-105 Intuitionistic Fuzzy Approximately Additive Mappings....Pages 107-124 Generalized Hyers–Ulam Stability for General Quadratic Functional Equation in Quasi-Banach Spaces....Pages 125-138 Ulam Stability Problem for Frames....Pages 139-152 Generalized Hyers–Ulam Stability of a Quadratic Functional Equation....Pages 153-164 On the Hyers–Ulam–Rassias Stability of the Bi-Pexider Functional Equation....Pages 165-175 Approximately Midconvex Functions....Pages 177-190 The Hyers–Ulam and Ger Type Stabilities of the First Order Linear Differential Equations....Pages 191-199 On the Butler–Rassias Functional Equation and its Generalized Hyers–Ulam Stability....Pages 201-206 A Note on the Stability of an Integral Equation....Pages 207-222 On the Stability of Polynomial Equations....Pages 223-227 Isomorphisms and Derivations in Proper JCQ * -Triples....Pages 229-245 Fuzzy Stability of an Additive-Quartic Functional Equation: A Fixed Point Approach....Pages 247-260 Front Matter....Pages 1-1 Selections of Set-Valued Maps Satisfying Functional Inclusions on Square-Symmetric Grupoids....Pages 261-272 On Stability of Isometries in Banach Spaces....Pages 273-285 Ulam Stability of the Operatorial Equations....Pages 287-305 Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces....Pages 307-318 Stability of the Quadratic–Cubic Functional Equation in Quasi–Banach Spaces....Pages 319-336 μ-Trigonometric Functional Equations and Hyers–Ulam Stability Problem in Hypergroups....Pages 337-358 Front Matter....Pages 359-359 On Multivariate Ostrowski Type Inequalities....Pages 361-369 Ternary Semigroups and Ternary Algebras....Pages 371-416 Popoviciu Type Functional Equations on Groups....Pages 417-426 Norm and Numerical Radius Inequalities for Two Linear Operators in Hilbert Spaces: A Survey of Recent Results....Pages 427-490 Cauchy’s Functional Equation and Nowhere Continuous /Everywhere Dense Costas Bijections in Euclidean Spaces....Pages 491-508 On Solutions of Some Generalizations of the Goła̧b–Schinzel Equation....Pages 509-521 One-parameter Groups of Formal Power Series of One Indeterminate....Pages 523-545 On Some Problems Concerning a Sum Type Operator....Pages 547-554 Priors on the Space of Unimodal Probability Measures....Pages 555-561 Generalized Weighted Arithmetic Means....Pages 563-582 On Means Which are Quasi-Arithmetic and of the Beckenbach–Gini Type....Pages 583-597 Scalar Riemann–Hilbert Problem for Multiply Connected Domains....Pages 599-632 Hodge Theory for Riemannian Solenoids....Pages 633-657 On Solutions of a Generalization of the Goła̧b–Schinzel Functional Equation....Pages 659-670 Front Matter....Pages 359-359 On a Functional Equation Containing an Indexed Family of Unknown Mappings....Pages 671-687 Two-Step Iterative Method for Nonconvex Bifunction Variational Inequalities....Pages 689-696 On a Sincov Type Functional Equation....Pages 697-708 Invariance in Some Families of Means....Pages 709-717 On a Hilbert-Type Integral Inequality....Pages 719-725 An Extension of Hardy–Hilbert’s Inequality....Pages 727-738 A Relation to Hilbert’s Integral Inequality and a Basic Hilbert-Type Inequality....Pages 739-748 Erratum....Pages E1-E1 Functional Equations in Mathematical Analysis, dedicated to S.M. Ulam in honor of his 100th birthday, focuses on various important areas of research in mathematical analysis and related subjects, providing an insight into the study of numerous nonlinear problems. Among other topics, it supplies the most recent results on the solutions to the Ulam stability problem. ¡ The original stability problem was posed by S.M. Ulam in 1940 and concerned approximate homomorphisms. The pursuit of solutions to this problem, but also to its generalizations and/or modifications for various classes of equations and inequalities, is an expanding area of research, and has led to the development of what is now called the Hyers-Ulam stability theory. ¡ Comprised of contributions from eminent scientists and experts from the international mathematical community, the volume presents several important types of functional equations and inequalities and their applications in mathematical analysis, geometry, physics, and applied mathematics. It is intended for researchers and students in mathematics, physics, and other computational and applied sciences