On single-valuedness of set-valued maps satisfying linear inclusions
Kazimierz Nikodem and Dorian Popa
Source: Banach J. Math. Anal. Volume 3, Number 1 (2009), 44-51.
Abstract
In this paper we give some results on single-valuedness of set-valued maps satisfying linear inclusions.
Primary Subjects: 54C60
Secondary Subjects: 39B62, 26A51
Keywords: set-valued map; linear inclusion; single-valuedness; backward doubly stochastic differential equations
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bjma/1240336422
Mathematical Reviews number (MathSciNet):
MR2461745
Zentralblatt MATH identifier:
1163.26353
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.
Mathematical Reviews (MathSciNet):
MR1048347
C. Berge, Espaces topologiques. Fonctions multivoques, Dunod, Paris, 1966.
Mathematical Reviews (MathSciNet):
MR105663
F. Deutsch and I. Singer, On single valuedness of convex set-valued maps, Set-Valued Analysis, 1 (1993), 97--103.
Mathematical Reviews (MathSciNet):
MR1230373
Digital Object Identifier: doi:10.1007/BF01039295
G. Godini, Set-valued Cauchy functional equation, Rev. Roumaine Math. Pures Appl., 20 (1975), 1113--1121.
Mathematical Reviews (MathSciNet):
MR393920
Z. Kominek, On $(a,b)$-convex functions, Arch. Math., 58 (1992), 64--69.
Mathematical Reviews (MathSciNet):
MR1139388
Digital Object Identifier: doi:10.1007/BF01198644
Zentralblatt MATH:
0754.26005
J. Matkowski and M. Pycia, On $(\alpha ,a)$-convex functions, Arch. Math., 64 (1995), 132--138.
Mathematical Reviews (MathSciNet):
MR1312001
Digital Object Identifier: doi:10.1007/BF01196632
Zentralblatt MATH:
0813.26004
J. Matkowski and W. Ślepak, On $(\alpha ,a)$-convex set-valued functions, Far East J. Math. Sci., 4 (2002), 85--89.
Mathematical Reviews (MathSciNet):
MR1899901
Zentralblatt MATH:
1018.54014
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.
Mathematical Reviews (MathSciNet):
MR1436269
Digital Object Identifier: doi:10.1007/BF02215969
Zentralblatt MATH:
0872.26008
D. Popa, On single valuedness of some classes of set valued maps, Automat. Comput. Appl. Math., 6 (2) (1997), 46--49.
Mathematical Reviews (MathSciNet):
MR1887369
D. Popa and N. Vornicescu, Locally compact set-valued solutions for the general linear equation, Aequationes Math., 67 (2004), 205--215.
Mathematical Reviews (MathSciNet):
MR2162227
Digital Object Identifier: doi:10.1007/s00010-003-2699-1
Zentralblatt MATH:
1054.39016
A. Roberts and D. Varberg, Convex functions, Academic Press, 1973.
Mathematical Reviews (MathSciNet):
MR442824
R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970.
Mathematical Reviews (MathSciNet):
MR274683
W. Smajdor, Superadditive set-valued functions and Banach-Steinhaus theorem, Radovi Matematicki, 3 (1987), 203--214.
Mathematical Reviews (MathSciNet):
MR931975
Zentralblatt MATH:
0654.39007
A. Száz, G. Száz, Additive relations, Publ. Math. Debrecen, 20 (1973), 259--272.
Mathematical Reviews (MathSciNet):
MR340878
Zentralblatt MATH:
0362.08002
A. Száz and G. Száz, Linear relations, Publ. Math. Debrecen, 27 (1980), 219--227.
Mathematical Reviews (MathSciNet):
MR603995
D.H. Tan, A note on multivalued affine mappings, Studia Univ. Babes-Bolyai, Mathematica, 33 (1988), 55--59.
Mathematical Reviews (MathSciNet):
MR1028753
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