Remarks on the Cauchy functional equation and variations of it View Full Text


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Article Info

DATE

2017-04

AUTHORS

Daniel Reem

ABSTRACT

This paper examines various aspects related to the Cauchy functional equation f(x+y)=f(x)+f(y), a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation. More... »

PAGES

237-264

References to SciGraph publications

  • 1996-02. Regularization and general methods in the theory of functional equations in AEQUATIONES MATHEMATICAE
  • 2005. Regularity Properties of Functional Equations in Several Variables in NONE
  • 2009-10. A new approach to the stability of linear functional operators in AEQUATIONES MATHEMATICAE
  • 2008-06. Stability of the Cauchy equation almost everywhere in AEQUATIONES MATHEMATICAE
  • 2008-06. A result of Tosio Aoki about a generalization of Hyers–Ulam stability of additive functions – a question of priority in AEQUATIONES MATHEMATICAE
  • 1936-12. Une remarque sur les équations fonctionnelles in COMMENTARII MATHEMATICI HELVETICI
  • 2000. Ulam’s Problem, Hyers’s Solution — and to Where They Led in FUNCTIONAL EQUATIONS AND INEQUALITIES
  • 1998. Stability of Functional Equations in Several Variables in NONE
  • 1988-02. On stability of the Cauchy equation on semigroups in AEQUATIONES MATHEMATICAE
  • 2009. Functional Equations and Inequalities with Applications in NONE
  • 2012-07. Stability of a conditional Cauchy equation in AEQUATIONES MATHEMATICAE
  • 1971-06. Extensions of certain homomorphisms of subsemigroups to homomorphisms of groups in AEQUATIONES MATHEMATICAE
  • 1989-06. Regularity properties of functional equations and inequalities in AEQUATIONES MATHEMATICAE
  • 1963. Abstract Harmonic Analysis in NONE
  • 2009. An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality in NONE
  • 1905-09. Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung:f(x+y)=f(x)+f(y) in MATHEMATISCHE ANNALEN
  • 1992-10. Approximate homomorphisms in AEQUATIONES MATHEMATICAE
  • 1995-08. Hyers-Ulam stability of functional equations in several variables in AEQUATIONES MATHEMATICAE
  • 1985. Cauchy functional equation on a restricted domain and commuting functions in ITERATION THEORY AND ITS FUNCTIONAL EQUATIONS
  • 2007-09. On the general theory of the Cauchy type functional equations with applications in analysis in AEQUATIONES MATHEMATICAE
  • 2013. Measure Theory, Second Edition in NONE
  • 1978-02. Functional equations on restricted domains in AEQUATIONES MATHEMATICAE
  • 1971-06. Regularity properties of functional equations in AEQUATIONES MATHEMATICAE
  • 1986-12. Christensen measurable solutions of generalized Cauchy functional equations in AEQUATIONES MATHEMATICAE
  • 1971-06. Measurability and continuity for a functional equation on a topological group in AEQUATIONES MATHEMATICAE
  • 1880-03. Sur le théorème fondamental de la géométrie projective in MATHEMATISCHE ANNALEN
  • 1972-10. On the uniqueness of solutions of the functional equationϕ(x+f(x))=ϕ(x)+ϕ(f(x)) in AEQUATIONES MATHEMATICAE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00010-016-0463-6

    DOI

    http://dx.doi.org/10.1007/s00010-016-0463-6

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    https://app.dimensions.ai/details/publication/pub.1083692427


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