1. Alsina C., Garcia Roig J.L., On some inequalities characterizing the exponential function, Arch. Math., Brno 26 (1990), no. 2–3, 67–71.
2. Alsina C., Ger R., On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2 (1998), no. 4, 373–380.
3. Azócar A., Giménez J., Nikodem K., Sánchez J.L., On strongly midconvex functions, Opuscula Math. 31 (2011), 15–26.
4. Baker, J.A., An analogue of the wave equation and certain related functional equations, Canad. Math. Bull. 12 (1969), 837–846.
5. Baker J.A., The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), 411–416.
6. Baron K., Matkowski J., Nikodem K., A sandwich with convexity, Math. Pannon. 5 (1994), 139–144.
7. Bernstein F., Doetsch G., Zur Theorie der konvexen Funktionen, Math. Ann. 76 (1915), 514–526.
8. Boros Z., Páles Zs., $\mathbb{Q}$-subdifferential of Jensen-convex functions, J. Math. Anal. Appl. 321 (2006), 99–113.
9. Bourbăcuţ N., Problem 11641, Amer. Math. Monthly 119 (2012), 345.
10. Daroczy Z., On the equality and comparison problem of a class of mean values, Aequationes Math. 81 (2011), 201–208.
11. Dinghas A., Zur Theorie der gewöhnlichen Differentialgleichungen, Ann. Acad. Sci. Fennicae, Ser. A I 375 (1966).
12. Fechner W., Some inequalities connected with the exponential function, Arch. Math., Brno 44 (2008), no. 3, 217–222.
13. Fechner W., On some functional inequalities related to the logarithmic mean, Acta Math. Hung. 128 (2010), no. 1–2, 36–45.
14. Fechner W., Functional inequalities and equivalences of some estimates, in: Inequalities and Applications 2010, dedicated to the Memory of Wolfgang Walter, Hajdúszoboszló, Hungary International Series of Numerical Mathematics 161, Birkhäuser, Basel, 2012, pp. 231–240.
15. Fechner W., Ger R., Some stability results for equations and inequalities connected with the exponential functions, in: Functional Equations and Difference Inequalities and Ulam Stability Notions (F.U.N.), Mathematics Research Developments, Nova Science Publishers Inc., New York, 2010, pp. 37–46.
16. Ger R., Nikodem K., Strongly convex functions of higher order, Nonlinear Anal. 74 (2011), 661–665.
17. Ger R., Šemrl P., The stability of the exponential equation, Proc. Amer. Math. Soc. 124 (1996), 779–787.
18. Gilányi A., Páles Zs., On Dinghas-type derivatives and convex functions of higher order, Real Anal. Exchange 27 (2001/2002), 485–493.
19. Girgensohn R., Lajkó K., A functional equation of Davison and its generalization, Aequationes Math. 60 (2000), 219–222.
20. Hopf E., Über die Zusammenhänge zwischen gewissen höheren Differenzenquotienten reeller Funktionen einer reellen Variablen und deren Differenzierbarkeitseigenschaften, Diss., Friedrich Wilhelms Universität Berlin, 1926.
21. Kominek Z., Kuczma M., Theorems of Bernstein–Doetsch, Piccard and Mehdi and semilinear topology, Arch. Math. (Basel) 52 (1989), 595–602.
22. Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Second Edition, ed. by Gilányi A., Birkhäuser Verlag, Basel, 2009.
23. Laczkovich M., Székelyhidi G., Harmonic analysis on discrete abelian groups, Proc. Amer. Math. Soc. 133 (2005), 1581–1586.
24. Maksa Gy., Rätz J., Remark 5 in: Proceedings of the 19th ISFE, Nantes–La Turballe, France 1981, Centre for Information Theory, Univ. of Waterloo, 1981.
25. Mureńko A., A generalization of Bernstein–Doetsch theorem, Demonstratio Math. 45 (2012), 35–38.
26. Popoviciu T., Sur quelques propriétés des fonctions d’une ou de deux variables réelles, Mathematica (Cluj) 8 (1934), 1–85.
27. Székelyhidi L., On a class of linear functional equations, Publ. Math. (Debrecen) 29 (1982), 19–28.
28. Varga A., On additive solutions of a linear equation, Acta Math Hungar. 128 (2010), 15–25.
29. Varga A., Vincze Cs., On a functional equation containing weighted arithmetic means, International Series of Numerical Mathematics 157 (2009), 305–315.
30. Varga A., Vincze Cs., On Daróczy’s problem for additive functions, Publ. Math. Debrecen 75 (2009), 299–310.
31. Veselý L., Zajiček L., Delta-convex mappings between Banach spaces and applications, Dissertationes Math. 289, Polish Scientific Publishers, Warszawa, 1989. Google Scholar