References
Bernstein, F. andDoetsch, G.,Zue Theorie der konvexen Funktionen. Math. Ann.76 (1915), 514–526.
Dubikajtis, L., Ferens, C., Ger, R. andKuczma, M.,On Mikusiński's functional equation Ann. Polon. Math.28 (1973), 39–47.
Ger, R.,Some remarks on convex functions. Fund. Math.66 (1970), 255–262.
Ger, R.,Some new conditions of continuity of convex functions. Mathematica (Clui)12 (35) (1970), 271–277.
Ger, R. andKuczma, M.,On the boundedness of continuity of convex functions and additive functions. Aequationes Math.4 (1970), 157–162.
Halmos, P. R.,Measure theory. Van Nostrand, New York, 1950.
Kemperman, J. H. B.,A general functional equation. Trans. Amer. Math. Soc.86 (1957), 28–56.
Kominek, Z.,On the sum and difference of two sets in topological vector spaces. Fund. Math.71 (1971), 165–169.
Kominek, Z.,Some generalization of the theorem of S. Picard. Prace Nauk. Uniw. Śląsk. Katowic.37 (1973), 31–33.
Kuczma, M.,Note on convex functions. Ann. Univ. Sci. Budapest. Sect. Math.2 (1959), 25–26.
Kuczma, M.,Some remarks on convexity and monotonicity. Rev. Roum. Math. Pures Appl.15 (1970), 1463–1469.
Kuczma, M.,Convex functions. InFunctional equations and inequalities. (Corso tenuto a La Mendola (Trento) dal 20 al 28 agosto 1970). Edizioni Cremonese, Roma 1971, pp. 195–213.
Kuczma, M. E.,On discontinuous additive functions. Fund. Math.66 (1970), 383–392.
Kuczma, M. E. andKuczma, M.,An elementary proof and an extension of a theorem of Steinhaus. Glasnik Mat.6 (26) (1971), 11–18.
Kurepa, S.,Convex functions. Glaskik Mat. Fiz. Astronom. Ser. II11 (1956), 89–93.
Mehdi, M. R.,On convex functions. J. London Math. Soc.39 (1964), 321–326.
Nagy, B.,On a generalization of the Cauchy equation. Aequationes Math.10 (1974), 165–171.
Ostrowski, A.,Über die Funktionalgleichung der Exponentialfunktion und verwandte Funktionalgleichungen. Jahresber. Deutsch. Math. Verein.38 (1929), 54–62.
Picard, S.,Sur des ensembles parfaits. Paris, 1942.
Roberts, A. W. andVarberg, D. E.,Convex functions. Academic Press, New York, 1973.
Sierpiński, W.,Sur les fonctions convexes mesurables. Fund. Math.1 (1920), 125–128.
Steinhaus, H.,Sur les distance des points des ensembles de mesure positive. Fund. Math.1 (1920), 93–104.
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Nikodem, K. On convex stochastic processes. Aeq. Math. 20, 184–197 (1980). https://doi.org/10.1007/BF02190513
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DOI: https://doi.org/10.1007/BF02190513