2022/03/31 by Tibor Kiss, Kiss, Tibor · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2203.16862
openalex publication_date 2022/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main result of the present paper is about the solutions of the functional equation \Eq* F(\fracx+y2)+f1(x)+f2(y)=G(g1(x)+g2(y)), x,y∈ I, derived originally, in a natural way, from the invariance problem of generalized weighted quasi-arithmetic means, where F,f1,f2,g1,g2:I→ℝ and G:g1(I)+g2(I)→ℝ are the unknown functions assumed to be continuously differentiable with 0∉ g'1(I)∪ g'2(I), and the set I stands for a nonempty open subinterval of ℝ. In addition to these, we will also touch upon solutions not necessarily regular. More precisely, we are going to solve the above equation assuming first that F is affine on I and g1 and g2 are continuous functions strictly monotone in the same sense, and secondly that g1 and g2 are invertible affine functions with a common additive part.