References
Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York-London, 1966.
Baker, J. A.,Some functional equations in topological groups and vector spaces. Ph.D. dissertation, University of Waterloo, 1968.
Buche, A. B. andBharucha-Reid, A. T.,On the generalized semigroup relation in the strong operator topology. Nederl. Akad. Wetensch. Indag. Math.33 (1971), 26–31.
Drobot, V.,Generalized Cauchy equations on groups. Aequationes Math.5 (1970), 120–122.
Dunford, N. andHille, E.,The differentiability and uniqueness of continuous solutions of addition formulas. Bull. Amer. Math. Soc.53 (1947), 799–805.
Hille, E. andPhillips, R. S.,Functional analysis and semi-groups. InAmer. Math. Soc. Colloq. Publ. Vol. 31. Rev. ed. Amer. Math. Soc., Providence, R.I., 1957.
Kurepa, S.,On some functional equations in Banach spaces. Studia Math.19 (1960), 149–158.
Kurepa, S.,A cosine functional equation in Banach algebras. Acta Sci. Math., Szeged23 (1962), 255–267.
Miyadera, I.,On one-parameter semi-groups of operators. J. Math. Tokyo1 (1951), 23–26.
Phillips, R. S.,On one-parameter semi-groups of linear transformations. Proc. Amer. Math. Soc.2 (1951), 234–237.
Yosida, K.,Functional analysis. InDie Grundlehren der Mathematischen Wissenschaften, Band 123. Springer-Verlag, Berlin-Heidelberg-New York, 1965.
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Buche, A.B., Vasudeva, H.L. The generalized cauchy equation for operator-valued functions. Aeq. Math. 14, 387–390 (1976). https://doi.org/10.1007/BF01835986
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DOI: https://doi.org/10.1007/BF01835986