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On selections of some generalized set-valued inclusions. (English) Zbl 1443.39015
Rassias, Themistocles M. (ed.) et al., Mathematical analysis and applications. Cham: Springer. Springer Optim. Appl. 154, 205-216 (2019).
The authors determine some conditions for which a set-valued function satisfying certain inclusions admits a unique selection satisfying the corresponding functional equation.
For the entire collection see [Zbl 1432.65003].
MSC:
39B52 Functional equations for functions with more general domains and/or ranges
40D25 Inclusion and equivalence theorems in summability theory
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[1] W. Smajdor, Superadditive set-valued functions. Glas. Mat. 21 (1986), 343-348 · Zbl 0617.26010
[2] Z. Gajda, R. Ger, Subadditive multifunctions and Hyers-Ulam stability. Numer. Math. 80, 281-291 (1987) · Zbl 0639.39014
[3] D. Popa, Additive selections of (α, β)-subadditive set valued maps. Glas. Mat. Ser. III 36, 11-16 (2001) · Zbl 1039.28013
[4] J. Brzdȩk, D. Popa, B. Xu, Selections of set-valued maps satisfying a linear inclusion in a single variable. Nonlin. Anal. 74, 324-330 (2011) · Zbl 1205.39025
[5] D. Inoan, D. Popa, On selections of generalized convex set-valued maps. Aequat. Math. 88, 267-276 (2014) · Zbl 1308.54017
[6] H. Khodaei, On the stability of additive, quadratic, cubic and quartic set-valued functional equations. Results Math. 68, 1-10 (2015) · Zbl 1330.39029
[7] G. Lu, C. Park, Hyers-Ulam stability of additive set-valued functional equations. Appl. Math. Lett. 24, 1312-1316 (2011) · Zbl 1220.39030
[8] K. Nikodem, On quadratic set-valued functions. Publ. Math. Debrecen 30, 297-301 (1984) · Zbl 0537.39002
[9] K. Nikodem, D. Popa, On selections of general linear inclusions. Publ. Math. Debrecen 75, 239-249 (2009) · Zbl 1212.39041
[10] K. Nikodem, D. Popa, On single-valuedness of set-valued maps satisfying linear inclusions. Banach J. Math. Anal. 3, 44-51 (2009) · Zbl 1163.26353
[11] C. Park, D. O’Regan, R. Saadati, Stability of some set-valued functional equations. Appl. Math. Lett. 24, 1910-1914 (2011) · Zbl 1236.39034
[12] M. Piszczek, On selections of set-valued inclusions in a single variable with applications to several variables. Results Math. 64, 1-12 (2013) · Zbl 1277.39032
[13] M. Piszczek, The properties of functional inclusions and Hyers-Ulam stability. Aequat. Math. 85, 111-118 (2013) · Zbl 1271.39031
[14] D. Popa, A property of a functional inclusion connected with Hyers-Ulam stability. J. Math. Inequal.4, 591-598 (2009) · Zbl 1189.39032
[15] K. Nikodem, K-Convex and K-Concave Set-Valued Functions, Zeszyty Naukowe, Politech, Krakow, 1989
[16] H. Rådström, An embedding theorem for space of convex sets. Proc. Am. Math. Soc. 3, 165-169 (1952) · Zbl 0046.33304
[17] W. Smajdor, Subadditive and subquadratic set-valued functions, Prace Nauk. Uniw. Śla̧sk, 889, Katowice (1987) · Zbl 0626.54019
[18] R. Urbański, A generalization of the Minkowski-Rådström-Hörmander theorem. Bull. Polish Acad. Sci. 24, 709-715 (1976) · Zbl 0336.46009
[19] M.E. Gordji, Z. Alizadeh, H. Khodaei, C. Park, On approximate homomorphisms: a fixed point approach. Math. Sci. 6, 59 (2012) · Zbl 1271.39023
[20] J.H. Bae, W.G. Park, A functional equation having monomials as solutions. Appl. Math. Comput. 216, 87-94 (2010) · Zbl 1191.39026
[21] M.E. Gordji, Z. Alizadeh, Y.J. Cho, H. Khodaei, On approximate C^∗-ternary m-homomorphisms: a fixed point approach. Fixed Point Theory Appl. (2011), Art. ID 454093 · Zbl 1216.39036
[22] Y.S. Lee, S.Y. Chung, Stability of quartic functional equation in the spaces of generalized functions. Adv. Differ. Equ. (2009), Art. ID 838347
[23] F.P. Greenleaf, Invariant Mean on Topological Groups and their Applications, Van Nostrand Mathematical Studies, vol. 16, New York/Toronto/London/Melbourne, 1969 · Zbl 0174.19001
[24] R. Badora, R. Ger, Z. Páles, Additive selections and the stability of the Cauchy functional equation. ANZIAM J. 44, 323-337 (2003) · Zbl 1037.39008
[25] R.
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