Sandwich theorems for radiant functions

Authors

  • Costică Mustăța Tiberiu Popoviciu Institute of Numerical Analysis, Romania

DOI:

https://doi.org/10.33993/jnaat441-1050

Keywords:

sandwich theorems, radiant functions, coradiant functions
Abstract views: 414

Abstract

We show that between two graphs, one of a radiant function and the other  of a coradiant, both dened 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.

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References

K. Baron, J. Matkowski and K. Nikodem, A Sandwich with convexity, Mathematica Panonica, 5 (1994) no. 1, pp. 139-144.

W. Förg-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. http://doi.org/10.2307/1995044 DOI: https://doi.org/10.1090/S0002-9947-1970-0415289-8

E.J. McShane, Extension of range of functions, Bull. Amer. Math. Soc.,40 (1934), pp. 837-842. http://doi.org/10.1090/S0002-9904-1934-05978-0 DOI: https://doi.org/10.1090/S0002-9904-1934-05978-0

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, Théor. Approx., 30 (2001) no. 1, pp. 61-67. http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art8

C. Mustata, On the extensions preserving the shape of semi-Hölder function, Results. Math., 63 (2013), pp. 425-433. http://doi.org/10.1007/s00025-011-0206-x DOI: https://doi.org/10.1007/s00025-011-0206-x

K. Nikodem and S. Wasowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math.,49 (1995), pp. 160-164. http://doi.org/10.1007/BF01827935 DOI: https://doi.org/10.1007/BF01827935

A.M. Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publisher, Boston-Dordrecht London, 2000. DOI: https://doi.org/10.1007/978-1-4757-3200-9

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. http://doi.org/10.1016/j.jmaa.2011.01.061 DOI: https://doi.org/10.1016/j.jmaa.2011.01.061

A. Szaz, The infimal convolution can be used to derive extensions theorems from sandwich ones, Acta Sci. Math. (Szeged), 76 (2010), pp. 489-499. DOI: https://doi.org/10.1007/BF03549839

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Published

2015-12-18

How to Cite

Mustăța, C. (2015). Sandwich theorems for radiant functions. J. Numer. Anal. Approx. Theory, 44(1), 81–90. https://doi.org/10.33993/jnaat441-1050

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