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- Title
A Pexider equation containing the aritmetic mean.
- Authors
Kiss, Tibor
- Abstract
In this paper we determine the solutions (φ , f 1 , f 2) of the Pexider functional equation φ ( x + y 2) (f 1 (x) - f 2 (y)) = 0 , (x , y) ∈ I 1 × I 2 , where I 1 and I 2 are nonempty open subintervals. Special cases of the above equation regularly arise in problems with two-variable means. We show that, under a rather weak regularity condition, the coordinate-functions of a typical solution of the equation are constant over several subintervals of their domain. The regularity condition in question will be that the set of zeros of φ is closed. We also discuss particular solutions where this condition is not met.
- Subjects
FUNCTIONAL equations; EQUATIONS; ARITHMETIC mean; INTEGRAL inequalities
- Publication
Aequationes Mathematicae, 2024, Vol 98, Issue 2, p579
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-023-00966-x