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2009 On single-valuedness of set-valued maps satisfying linear inclusions
Kazimierz Nikodem, Dorian Popa
Banach J. Math. Anal. 3(1): 44-51 (2009). DOI: 10.15352/bjma/1240336422
Abstract

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

References

1.

J. Aczél, Lectures on Functional Equations and Their Applications, Dover Publications Inc., Mineola, New York, 2006.J. Aczél, Lectures on Functional Equations and Their Applications, Dover Publications Inc., Mineola, New York, 2006.

2.

J.P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser, Boston-Basel-Berlin, 1990. MR1048347J.P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser, Boston-Basel-Berlin, 1990. MR1048347

3.

C. Berge, Espaces topologiques. Fonctions multivoques, Dunod, Paris, 1966. MR105663C. Berge, Espaces topologiques. Fonctions multivoques, Dunod, Paris, 1966. MR105663

4.

F. Deutsch and I. Singer, On single valuedness of convex set-valued maps, Set-Valued Analysis, 1 (1993), 97–103. MR1230373 10.1007/BF01039295 0807.46011F. Deutsch and I. Singer, On single valuedness of convex set-valued maps, Set-Valued Analysis, 1 (1993), 97–103. MR1230373 10.1007/BF01039295 0807.46011

5.

G. Godini, Set-valued Cauchy functional equation, Rev. Roumaine Math. Pures Appl., 20 (1975), 1113–1121. MR393920G. Godini, Set-valued Cauchy functional equation, Rev. Roumaine Math. Pures Appl., 20 (1975), 1113–1121. MR393920

6.

Z. Kominek, On $(a,b)$-convex functions, Arch. Math., 58 (1992), 64–69. MR1139388 10.1007/BF01198644 0754.26005Z. Kominek, On $(a,b)$-convex functions, Arch. Math., 58 (1992), 64–69. MR1139388 10.1007/BF01198644 0754.26005

7.

J. Matkowski and M. Pycia, On $(\alpha ,a)$-convex functions, Arch. Math., 64 (1995), 132–138. MR1312001 10.1007/BF01196632 0813.26004J. Matkowski and M. Pycia, On $(\alpha ,a)$-convex functions, Arch. Math., 64 (1995), 132–138. MR1312001 10.1007/BF01196632 0813.26004

8.

J. Matkowski and W. Ślepak, On $(\alpha ,a)$-convex set-valued functions, Far East J. Math. Sci., 4 (2002), 85–89. MR1899901 1018.54014J. Matkowski and W. Ślepak, On $(\alpha ,a)$-convex set-valued functions, Far East J. Math. Sci., 4 (2002), 85–89. MR1899901 1018.54014

9.

K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. \Lódz. Mat. 559, Rozprawy Nauk. 114, \Lódz, 1989.K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. \Lódz. Mat. 559, Rozprawy Nauk. 114, \Lódz, 1989.

10.

K. Nikodem, F. Papalini and S. Vercillo, Some representations of midconvex set-valued functions, Aequationes Math., 53 (1997), 127–140. MR1436269 10.1007/BF02215969 0872.26008K. Nikodem, F. Papalini and S. Vercillo, Some representations of midconvex set-valued functions, Aequationes Math., 53 (1997), 127–140. MR1436269 10.1007/BF02215969 0872.26008

11.

D. Popa, On single valuedness of some classes of set valued maps, Automat. Comput. Appl. Math., 6 (2) (1997), 46–49. MR1887369D. Popa, On single valuedness of some classes of set valued maps, Automat. Comput. Appl. Math., 6 (2) (1997), 46–49. MR1887369

12.

D. Popa and N. Vornicescu, Locally compact set-valued solutions for the general linear equation, Aequationes Math., 67 (2004), 205–215. MR2162227 10.1007/s00010-003-2699-1 1054.39016D. Popa and N. Vornicescu, Locally compact set-valued solutions for the general linear equation, Aequationes Math., 67 (2004), 205–215. MR2162227 10.1007/s00010-003-2699-1 1054.39016

13.

A. Roberts and D. Varberg, Convex functions, Academic Press, 1973. MR442824A. Roberts and D. Varberg, Convex functions, Academic Press, 1973. MR442824

14.

R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970. MR274683R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970. MR274683

15.

W. Smajdor, Superadditive set-valued functions and Banach-Steinhaus theorem, Radovi Matematicki, 3 (1987), 203–214. MR931975 0654.39007W. Smajdor, Superadditive set-valued functions and Banach-Steinhaus theorem, Radovi Matematicki, 3 (1987), 203–214. MR931975 0654.39007

16.

A. Száz, G. Száz, Additive relations, Publ. Math. Debrecen, 20 (1973), 259–272. MR340878 0362.08002A. Száz, G. Száz, Additive relations, Publ. Math. Debrecen, 20 (1973), 259–272. MR340878 0362.08002

17.

A. Száz and G. Száz, Linear relations, Publ. Math. Debrecen, 27 (1980), 219–227. MR603995A. Száz and G. Száz, Linear relations, Publ. Math. Debrecen, 27 (1980), 219–227. MR603995

18.

D.H. Tan, A note on multivalued affine mappings, Studia Univ. Babes-Bolyai, Mathematica, 33 (1988), 55–59. MR1028753D.H. Tan, A note on multivalued affine mappings, Studia Univ. Babes-Bolyai, Mathematica, 33 (1988), 55–59. MR1028753
Copyright © 2009 Tusi Mathematical Research Group
Kazimierz Nikodem and Dorian Popa "On single-valuedness of set-valued maps satisfying linear inclusions," Banach Journal of Mathematical Analysis 3(1), 44-51, (2009). https://doi.org/10.15352/bjma/1240336422
Published: 2009
Vol.3 • No. 1 • 2009
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