37 results on '"Zeglami, D."'
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2. A class of semigroup homomorphisms arising from the product in a pure quartic number field
3. Matrix homomorphism equations on a class of monoids and non Abelian groupoids
4. On a class of functional equations which includes the Pexider's one
5. Wilson’s functional equation with an anti-endomorphism
6. Nice results about quadratic type functional equations on semigroups
7. Solution of Generalized Jensen and Quadratic Functional Equations
8. A Functional Equation Originated from the Product in a Cubic Number Field
9. D’Alembert’s Matrix Functional Equation with an Endomorphism on Abelian Groups
10. On Gajda’s type quadratic equation on a locally compact abelian group
11. Solution of several functional equations on abelian groups with involution
12. D’Alembert’s Functional Equation and Superstability Problem in Hypergroups
13. μ-Trigonometric Functional Equations and Hyers–Ulam Stability Problem in Hypergroups : Trigonometric Formulas on Hypergroups
14. Functional equations on semigroups with an endomorphism
15. Integral functional equations on locally compact groups with involution
16. Some functional equations related to number theory
17. Superstability problem for a large class of functional equations
18. On a variant of μ-Wilson’s functional equation on a locally compact group
19. The superstability of a variant of Wilson’s functional equation on an arbitrary group
20. Hyers–Ulam stability of generalized Wilson’s and d’Alembert’s functional equations
21. D’Alembert’s Functional Equation and Superstability Problem in Hypergroups
22. μ-Trigonometric Functional Equations and Hyers–Ulam Stability Problem in Hypergroups
23. Wilson’s functional equation with an anti-endomorphism
24. On the stability of a class of Cosine type functional equations
25. Nice results about quadratic type functional equations on semigroups
26. The integral sine addition law
27. A sine type functional equation on a topological group
28. An integral functional equation on groups under two measures
29. A variant of the quadratic functional equation on semigroups
30. The generalized Van Vleck's equation on locally compact groups
31. Solution of several functional equations on abelian groups with involution.
- Abstract
Let
G be a locally compact abelian Hausdorff group, let σbe a continuous involution on G , and let μ,νbe regular, compactly supported, complex-valued Borel measures on G . We determine the continuous solutions f,g:G→Cof each of the two functional equations ∫Gf(x+y+t)dμ(t)+∫Gf(x+σ(y)+t)dν(t)=f(x)g(y),x,y∈G,∫Gf(x+y+t)dμ(t)+∫Gf(x+σ(y)+t)dν(t)=g(x)f(y),x,y∈G, in terms of characters and additive functions. These equations provides a common generalization of many functional equations such as d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Van Vleck’s, or Wilson’s equations. So, several functional equations will be solved. [ABSTRACT FROM AUTHOR]
32. Superstability problem for a large class of functional equations
33. The superstability of a variant of Wilson’s functional equation on an arbitrary group
34. On the Superstability of a Generalization of the Cosine Equation
35. On the Superstability of Trigonometric Type Functional Equations
36. Hyers–Ulam stability of generalized Wilson’s and d’Alembert’s functional equations
37. D'Alembert's functional equations on hypergroups
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