We show that between two graphs, one of a radiant function and the other of a coradiant, both defined on a real interval containing 0, there exists at least one line which separates the graphs. The conditions for the uniqueness of a separating linear function are also established.
Tiberiu Popoviciu Institute of Numerical Analysis, Romania
Sandwich theorems; radiant functions; coradiant functions.
C. Mustăța, Sandwich theorems for radiant functions, J. Numer. Anal. Approx. Theory, 44 (2015) no. 1, 81-90.
Journal Numer. Anal.Approx. Theory
Publishing house of the Romanian Academy
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 K. Baron, J. Matkowski and K. Nikodem, A Sandwich with convexity, Mathematica Panonica, 5 (1994) no. 1, pp. 139–144.
 W. Forg-Rob, K. Nicodem and Z. Pales, Separation by monotonic functions, Mathematica Panonica, 7 (1996) no. 2, pp. 191–196.
 B. Fuchssteiner and W. Lusky, Convex Cones, North Holland Math. Stud., 56 (North Holland, Amsterdam, 1981).
 J.A. Johnson, Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc., 148(1970), pp. 147–169.
 E.J. McShane, Extension of range of functions, Bull. Amer. Math. Soc., 40 (1934), pp. 837–842.
 C. Mustata, Norm preserving extension of starshaped Lipschitz functions, Mathematica (Cluj), 19(42)2 (1977), pp. 183–187.
 C. Mustata, Extensions of semi-Lipschitz functions on quasi-metric spaces, Rev. Anal. Numer, Theor. Approx., 30 (2001) no. 1, pp. 61–67.
 C. Mustata, On the extensions preserving the shape of semi-Holder function, Results. Math., 63 (2013), pp. 425–433.
 K. Nikodem and S. Wasowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math., 49 (1995), pp. 160–164.
 A.M. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publisher, Boston-Dordrecht-London, 2000.
 A.M. Rubinov and A.P. Shveidel, Radiant and star-shaped functions, Pacific Journal of Optimization, 3 (2007) no. 1, pp. 193–212.
 S. Simons, The asymmetric sandwich theorem, Journal of Convex Analysis, 20 (2013) no. 1, pp. 107–124.
 S. Suzuki and D. Kuroiwa, Sandwich theorem for quasiconvex functions and its applications, J. Math. Anal. Appl., 379 (2011), pp. 649–655.
 A. Szaz, The infimal convolution can be used to derive extensions theorems from sandwich ones, Acta Sci. Math. (Szeged), 76 (2010), pp. 489–499.