A characterization of functions with dense graph in the plane or half-plane
Abstract
Let R be the set of all real numbers. In the present paper we shall characterize functions f: R→R which are either linear or have graph contained and dense in the plane or half-plane determined by a linear function. For this purpose we consider functions satisfying certain limitary conditions which are related to the additivity equation but considerably weaker than that.
References
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GajdaZ. (1986). A characterization of functions with dense graph in the plane or half-plane. Annales Mathematicae Silesianae, 2, 37-46. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14319
Zbigniew Gajda
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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