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A Pexider equation containing the aritmetic mean.
- Source :
-
Aequationes Mathematicae . Apr2024, Vol. 98 Issue 2, p579-589. 11p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FUNCTIONAL equations
*EQUATIONS
*ARITHMETIC mean
*INTEGRAL inequalities
Subjects
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 98
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 176339614
- Full Text :
- https://doi.org/10.1007/s00010-023-00966-x