Abstract
We present some results on the existence of a unique selection of a set-valued function satisfying some generalized set-valued inclusions.
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References
W. Smajdor, Superadditive set-valued functions. Glas. Mat. 21 (1986), 343–348
Z. Gajda, R. Ger, Subadditive multifunctions and Hyers-Ulam stability. Numer. Math. 80, 281–291 (1987)
D. Popa, Additive selections of (α, β)-subadditive set valued maps. Glas. Mat. Ser. III 36, 11–16 (2001)
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)
D. Inoan, D. Popa, On selections of generalized convex set-valued maps. Aequat. Math. 88, 267–276 (2014)
H. Khodaei, On the stability of additive, quadratic, cubic and quartic set-valued functional equations. Results Math. 68, 1–10 (2015)
G. Lu, C. Park, Hyers-Ulam stability of additive set-valued functional equations. Appl. Math. Lett. 24, 1312–1316 (2011)
K. Nikodem, On quadratic set-valued functions. Publ. Math. Debrecen 30, 297–301 (1984)
K. Nikodem, D. Popa, On selections of general linear inclusions. Publ. Math. Debrecen 75, 239–249 (2009)
K. Nikodem, D. Popa, On single-valuedness of set-valued maps satisfying linear inclusions. Banach J. Math. Anal. 3, 44–51 (2009)
C. Park, D. O’Regan, R. Saadati, Stability of some set-valued functional equations. Appl. Math. Lett. 24, 1910–1914 (2011)
M. Piszczek, On selections of set-valued inclusions in a single variable with applications to several variables. Results Math. 64, 1–12 (2013)
M. Piszczek, The properties of functional inclusions and Hyers-Ulam stability. Aequat. Math. 85, 111–118 (2013)
D. Popa, A property of a functional inclusion connected with Hyers-Ulam stability. J. Math. Inequal.4, 591–598 (2009)
K. Nikodem, K-Convex and K-Concave Set-Valued Functions, Zeszyty Naukowe, Politech, Krakow, 1989
H. Rådström, An embedding theorem for space of convex sets. Proc. Am. Math. Soc. 3, 165–169 (1952)
W. Smajdor, Subadditive and subquadratic set-valued functions, Prace Nauk. Uniw. Śla̧sk, 889, Katowice (1987)
R. Urbański, A generalization of the Minkowski-Rådström-Hörmander theorem. Bull. Polish Acad. Sci. 24, 709–715 (1976)
M.E. Gordji, Z. Alizadeh, H. Khodaei, C. Park, On approximate homomorphisms: a fixed point approach. Math. Sci. 6, 59 (2012)
J.H. Bae, W.G. Park, A functional equation having monomials as solutions. Appl. Math. Comput. 216, 87–94 (2010)
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
Y.S. Lee, S.Y. Chung, Stability of quartic functional equation in the spaces of generalized functions. Adv. Differ. Equ. (2009), Art. ID 838347
F.P. Greenleaf, Invariant Mean on Topological Groups and their Applications, Van Nostrand Mathematical Studies, vol. 16, New York/Toronto/London/Melbourne, 1969
R. Badora, R. Ger, Z. Páles, Additive selections and the stability of the Cauchy functional equation. ANZIAM J. 44, 323–337 (2003)
R. Ger, The singular case in the stability behaviour of linear mappings. Grazer Math. Ber. 316, 59–70 (1992)
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Hayati, B., Khodaei, H., Rassias, T.M. (2019). On Selections of Some Generalized Set-Valued Inclusions. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_7
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DOI: https://doi.org/10.1007/978-3-030-31339-5_7
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