Abstract
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.
Authors
Costică Mustăța
Tiberiu Popoviciu Institute of Numerical Analysis, Romania
Keywords
Sandwich theorems; radiant functions; coradiant functions.
Paper coordinates
C. Mustăța, Sandwich theorems for radiant functions, J. Numer. Anal. Approx. Theory, 44 (2015) no. 1, 81-90.
About this paper
Journal
Journal Numer. Anal.Approx. Theory
Publisher Name
Publishing house of the Romanian Academy
Print ISSN
2457-6794
Online ISSN
2501-059X
google scholar link
[1] K. Baron, J. Matkowski and K. Nikodem, A Sandwich with convexity, Mathematica Panonica, 5 (1994) no. 1, pp. 139–144.
[2] W. Forg-Rob, K. Nicodem and Z. Pales, Separation by monotonic functions, Mathematica Panonica, 7 (1996) no. 2, pp. 191–196.
[3] B. Fuchssteiner and W. Lusky, Convex Cones, North Holland Math. Stud., 56 (North Holland, Amsterdam, 1981).
[4] J.A. Johnson, Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc., 148(1970), pp. 147–169.
[5] E.J. McShane, Extension of range of functions, Bull. Amer. Math. Soc., 40 (1934), pp. 837–842.
[6] C. Mustata, Norm preserving extension of starshaped Lipschitz functions, Mathematica (Cluj), 19(42)2 (1977), pp. 183–187.
[7] C. Mustata, Extensions of semi-Lipschitz functions on quasi-metric spaces, Rev. Anal. Numer, Theor. Approx., 30 (2001) no. 1, pp. 61–67.
[8] C. Mustata, On the extensions preserving the shape of semi-Holder function, Results. Math., 63 (2013), pp. 425–433.
[9] K. Nikodem and S. Wasowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math., 49 (1995), pp. 160–164.
[10] A.M. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publisher, Boston-Dordrecht-London, 2000.
[11] A.M. Rubinov and A.P. Shveidel, Radiant and star-shaped functions, Pacific Journal of Optimization, 3 (2007) no. 1, pp. 193–212.
[12] S. Simons, The asymmetric sandwich theorem, Journal of Convex Analysis, 20 (2013) no. 1, pp. 107–124.
[13] S. Suzuki and D. Kuroiwa, Sandwich theorem for quasiconvex functions and its applications, J. Math. Anal. Appl., 379 (2011), pp. 649–655.
[14] A. Szaz, The infimal convolution can be used to derive extensions theorems from sandwich ones, Acta Sci. Math. (Szeged), 76 (2010), pp. 489–499.