# Some results on stability and on characterization of K-convexity of set-valued functions

Tiziana Cardinali; Francesca Papalini

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 2, page 185-192
- ISSN: 0066-2216

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topTiziana Cardinali, and Francesca Papalini. "Some results on stability and on characterization of K-convexity of set-valued functions." Annales Polonici Mathematici 58.2 (1993): 185-192. <http://eudml.org/doc/262414>.

@article{TizianaCardinali1993,

abstract = {We present a stability theorem of Ulam-Hyers type for K-convex set-valued functions, and prove that a set-valued function is K-convex if and only if it is K-midconvex and K-quasiconvex.},

author = {Tiziana Cardinali, Francesca Papalini},

journal = {Annales Polonici Mathematici},

keywords = {set-valued functions; K-convex (K-midconvex, K-quasiconvex) set-valued functions; Ulam-Hyers stability; -convexity; stability of convex functions; - quasiconvexity},

language = {eng},

number = {2},

pages = {185-192},

title = {Some results on stability and on characterization of K-convexity of set-valued functions},

url = {http://eudml.org/doc/262414},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Tiziana Cardinali

AU - Francesca Papalini

TI - Some results on stability and on characterization of K-convexity of set-valued functions

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 2

SP - 185

EP - 192

AB - We present a stability theorem of Ulam-Hyers type for K-convex set-valued functions, and prove that a set-valued function is K-convex if and only if it is K-midconvex and K-quasiconvex.

LA - eng

KW - set-valued functions; K-convex (K-midconvex, K-quasiconvex) set-valued functions; Ulam-Hyers stability; -convexity; stability of convex functions; - quasiconvexity

UR - http://eudml.org/doc/262414

ER -

## References

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- [2] F. A. Behringer, Convexity is equivalent to midpoint convexity combined with strict quasiconvexity, Optimization (ed. K.-H. Elster, Ilmenau, Germany), 24 (1992), 219-228. Zbl0815.39009
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- [6] D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), 821-828. Zbl0047.29505
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- [8] N. Kuhn, A note on t-convex functions, in: General Inequalities 4 (Proc. Oberwolfach 1983), Internat. Ser. Numer. Math. 71, Birkhäuser, 1984, 269-276.
- [9] C. T. Ng and K. Nikodem, On approximately convex functions, Proc. Amer. Math. Soc., to appear. Zbl0823.26006
- [10]₁ K. Nikodem, Approximately quasiconvex functions, C. R. Math. Rep. Acad. Sci. Canada 10 (6) (1988), 291-294. Zbl0664.26006
- [10]₂ K. Nikodem, On some class of midconvex functions, Ann. Polon. Math. 50 (1989), 145-151. Zbl0706.39004
- [10]₃ K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódz. 559 (Rozprawy Mat. 114) (1989).
- [11] H. Rådström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
- [12] R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, N.J., 1970. Zbl0193.18401

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