The functional equation 𝑎𝑓(𝑎𝑥)+𝑏𝑓(𝑏𝑥+𝑎)=𝑏𝑓(𝑏𝑥)+𝑎𝑓(𝑎𝑥+𝑏) extensions and almost periodic solutions

Ryff, John V.

doi:10.1090/S0002-9904-1976-14043-8

Bulletin of the American Mathematical Society

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ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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The functional equation $af\left ( {ax} \right ) + bf\left ( {bx + a} \right ) = bf\left ( {bx} \right ) + af\left ( {ax + b} \right )$ extensions and almost periodic solutions
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Bull. Amer. Math. Soc. 82 (1976), 325-327

References

John V. Ryff, On the representation of doubly stochastic operators, Pacific J. Math. 13 (1963), 1379–1386. MR 163171, DOI 10.2140/pjm.1963.13.1379
John V. Ryff, Orbits of $L^{1}$-functions under doubly stochastic transformations, Trans. Amer. Math. Soc. 117 (1965), 92–100. MR 209866, DOI 10.1090/S0002-9947-1965-0209866-5
John V. Ryff, Extreme points of some convex subsets of $L^{1}(0,\,1)$, Proc. Amer. Math. Soc. 18 (1967), 1026–1034. MR 217586, DOI 10.1090/S0002-9939-1967-0217586-3
Yūji Sakai and Tetsuya Shimogaki, Equimeasurability of functions and doubly stochastic operators, K\B{o}dai Math. Sem. Rep. 24 (1972), 203–211. MR 308831
Ray C. Shiflett, Extreme Markov operators and the orbits of Ryff, Pacific J. Math. 40 (1972), 201–206. MR 302865, DOI 10.2140/pjm.1972.40.201