The stability of the exponential equation

DOI10.1090/S0002-9939-96-03031-6zbMath0846.39013OpenAlexW1501797494MaRDI QIDQ4875527

Roman Ger, Peter Šemrl

Publication date: 12 September 1996

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03031-6

zbMATH Keywords

stabilityexponential functionCauchy functional equationexponential equationcancellative Abelian semigroup

Mathematics Subject Classification ID

Functional equations for functions with more general domains and/or ranges (39B52) Systems of functional equations and inequalities (39B72)

Related Items (48)

Roman Ger, 70 years of a mathematician's adventurous life ⋮ Stability of a generalization of Wilson's equation ⋮ Hyers-Ulam stability of spherical functions ⋮ Stability problem for the composite type functional equations ⋮ The Hyers–Ulam–Aoki Type Stability of Some Functional Equations on Banach Lattices ⋮ Stability and common stability for the systems of linear equations and its applications ⋮ General stability of functional equations of linear type ⋮ A remark on a result of Schwaiger ⋮ On the superstability of the functional equation \(f(x^ y)=yf(x)\) ⋮ Continuity of iteration and approximation of iterative roots ⋮ Some new results on the superstability of the Cauchy equation on semigroups ⋮ On some recent developments in Ulam's type stability ⋮ Generalized Hyers-Ulam stability of trigonometric functional equations ⋮ Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups ⋮ Survey on Cauchy Functional Equation in Lattice Environments ⋮ Stability of functional equations in single variable. ⋮ Some functional equations originating from number theory ⋮ Investigating a Class of Nonlinear Fractional Differential Equations and Its Hyers-Ulam Stability by Means of Topological Degree Theory ⋮ Lipschitz stability of operators in Banach spaces ⋮ Stability of a functional equation connected with Reynolds operator ⋮ Ulam's type stability of involutional-exponential functional equations ⋮ Stability of the exponential functional equation in Riesz algebras ⋮ Solutions and stability of a variant of Wilson's functional equation ⋮ Stability problem for the Gołąb-Schinzel type functional equations ⋮ On stability of a functional equation connected with the Reynolds operator ⋮ Unnamed Item ⋮ On the stability of a multiplicative functional equation ⋮ Functional equation \(f(x)=pf(x - 1) - qf(x - 2)\) and its Hyers-Ulam stability ⋮ On approximately additive functions ⋮ Hyers-Ulam stability of linear differential equations of first order. ⋮ Exponential functional equation on spheres ⋮ Stability of the Banach space valued Chebyshev differential equation ⋮ On a Pexiderized conditional exponential functional equation ⋮ On the stability of a pexiderized Gołąb-Schinzel equation ⋮ On an asymptotic behavior of exponential functional equation ⋮ Solutions and stability of generalized Kannappan's and Van Vleck's functional equations ⋮ A note to establish the Hyers-Ulam stability for a nonlinear integral equation with Lipschitzian kernel ⋮ The Ulam stability problem for the functional equation \(f(x\star g(y))=f(x)f(y)\) ⋮ Richard’s inequality, Cauchy–Schwarz’s inequality, and approximate solutions of Sincov’s equation ⋮ On functions having Cauchy differences in some prescribed sets ⋮ Hyers-Ulam stability of linear differential equations of first order. III ⋮ Approximate solutions of the Gołąb-Schinzel equation ⋮ On the stability of functional equations in Banach spaces ⋮ Recent developments of the conditional stability of the homomorphism equation ⋮ Quotient stability of a class of composite equations ⋮ Orthogonalities and functional equations ⋮ Two general theorems on superstability of functional equations ⋮ Exponential stability of quasihomomorphisms into Banach algebras and a Ger-Šemrl theorem

Cites Work

• The stability of homomorphisms and amenability, with applications to functional equations
• On the functional equation \(F(x+y,z)+F(x,y)=F(x,y+z)+F(y,z)\)
• The Stability of the Cosine Equation
• The Stability of the Equation f(x + y) = f(x)f(y)
• Unnamed Item
• Unnamed Item

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