Ebook: Functional Equations in Mathematical Analysis

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.

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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.

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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.

Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Stability Properties of Some Functional Equations....Pages 3-13
Note on Superstability of Mikusi?ski’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
?-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 Go?a?b–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 Go?a?b–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

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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.

Content:
Front Matter....Pages i-xvii
Front Matter....Pages 1-1
Stability Properties of Some Functional Equations....Pages 3-13
Note on Superstability of Mikusi?ski’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
?-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 Go?a?b–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 Go?a?b–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
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