Solutions and Stability of Generalized Kannappan’s and Van Vleck’s Functional Equations
Copyright policy )Solutions and Stability of Generalized Kannappan’s and Van Vleck’s Functional Equations
Abstract We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations ∫Sf(xyt)dµ(t)+∫Sf(xσ(y)t)dµ(t)= 2f(x)f(y), x,y ∈ S; ∫Sf(xσ(y)t)dµ(t)-∫Sf(xyt)dµ(t)= 2f(x)f(y), x,y ∈ S; where S is a semigroup, σ is an involutive automorphism of S and µ is a linear combination of Dirac measures ( ᵟ zi)I ∈ I, such that for all i ∈ I, ziis in the center of S. We show that the solutions of these equations are closely related to the solutions of the d’Alembert’s classic functional equation with an involutive automorphism. Furthermore, we obtain the superstability theorems for these functional equations in the general case, where σ is an involutive morphism.
- Université Ibn Zohr Morocco
automorphism, Deformations and Structures of Hom-Lie Algebras, 39B82, 39B32, 39B52, Morphism, Semigroup, Stability, separation, extension, and related topics for functional equations, Functional equations for complex functions, Mathematical analysis, Kannappan’s equation, Van Vleck's equation, Differential equation, d’Alembert’s equation, complex measure, Machine learning, QA1-939, involution, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Functional equations for functions with more general domains and/or ranges, Hyers-Ulam stability, d'Alembert's equation, Stability (learning theory), Functional Equations, Algebra and Number Theory, Crystallography, Kannappan's equation, Applied Mathematics, Pure mathematics, multiplicative function, Stability of Functional Equations in Mathematical Analysis, Center (category theory), Automorphism, Computer science, Functional equation, Chemistry, Van Vleck’s equation, Mathematics - Classical Analysis and ODEs, semigroup, Mathematical physics, Physical Sciences, Mathematics
automorphism, Deformations and Structures of Hom-Lie Algebras, 39B82, 39B32, 39B52, Morphism, Semigroup, Stability, separation, extension, and related topics for functional equations, Functional equations for complex functions, Mathematical analysis, Kannappan’s equation, Van Vleck's equation, Differential equation, d’Alembert’s equation, complex measure, Machine learning, QA1-939, involution, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Functional equations for functions with more general domains and/or ranges, Hyers-Ulam stability, d'Alembert's equation, Stability (learning theory), Functional Equations, Algebra and Number Theory, Crystallography, Kannappan's equation, Applied Mathematics, Pure mathematics, multiplicative function, Stability of Functional Equations in Mathematical Analysis, Center (category theory), Automorphism, Computer science, Functional equation, Chemistry, Van Vleck’s equation, Mathematics - Classical Analysis and ODEs, semigroup, Mathematical physics, Physical Sciences, Mathematics
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