Banach Journal of Mathematical Analysis

On single-valuedness of set-valued maps satisfying linear inclusions

Kazimierz Nikodem and Dorian Popa

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Abstract

In this paper we give some results on single-valuedness of set-valued maps satisfying linear inclusions.

Article information

Source
Banach J. Math. Anal., Volume 3, Number 1 (2009), 44-51.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336422

Digital Object Identifier
doi:10.15352/bjma/1240336422

Mathematical Reviews number (MathSciNet)
MR2461745

Zentralblatt MATH identifier
1163.26353

Subjects
Primary: 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
Secondary: 39B62: Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx] 26A51: Convexity, generalizations

Keywords
set-valued map linear inclusion single-valuedness backward doubly stochastic differential equations

Citation

Nikodem, Kazimierz; Popa, Dorian. On single-valuedness of set-valued maps satisfying linear inclusions. Banach J. Math. Anal. 3 (2009), no. 1, 44--51. doi:10.15352/bjma/1240336422. https://projecteuclid.org/euclid.bjma/1240336422


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References

  • J. Aczél, Lectures on Functional Equations and Their Applications, Dover Publications Inc., Mineola, New York, 2006.
  • J.P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser, Boston-Basel-Berlin, 1990.
  • C. Berge, Espaces topologiques. Fonctions multivoques, Dunod, Paris, 1966.
  • F. Deutsch and I. Singer, On single valuedness of convex set-valued maps, Set-Valued Analysis, 1 (1993), 97–103.
  • G. Godini, Set-valued Cauchy functional equation, Rev. Roumaine Math. Pures Appl., 20 (1975), 1113–1121.
  • Z. Kominek, On $(a,b)$-convex functions, Arch. Math., 58 (1992), 64–69.
  • J. Matkowski and M. Pycia, On $(\alpha ,a)$-convex functions, Arch. Math., 64 (1995), 132–138.
  • J. Matkowski and W. Ślepak, On $(\alpha ,a)$-convex set-valued functions, Far East J. Math. Sci., 4 (2002), 85–89.
  • K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. \Lódz. Mat. 559, Rozprawy Nauk. 114, \Lódz, 1989.
  • K. Nikodem, F. Papalini and S. Vercillo, Some representations of midconvex set-valued functions, Aequationes Math., 53 (1997), 127–140.
  • D. Popa, On single valuedness of some classes of set valued maps, Automat. Comput. Appl. Math., 6 (2) (1997), 46–49.
  • D. Popa and N. Vornicescu, Locally compact set-valued solutions for the general linear equation, Aequationes Math., 67 (2004), 205–215.
  • A. Roberts and D. Varberg, Convex functions, Academic Press, 1973.
  • R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970.
  • W. Smajdor, Superadditive set-valued functions and Banach-Steinhaus theorem, Radovi Matematicki, 3 (1987), 203–214.
  • A. Száz, G. Száz, Additive relations, Publ. Math. Debrecen, 20 (1973), 259–272.
  • A. Száz and G. Száz, Linear relations, Publ. Math. Debrecen, 27 (1980), 219–227.
  • D.H. Tan, A note on multivalued affine mappings, Studia Univ. Babes-Bolyai, Mathematica, 33 (1988), 55–59.