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On the stability of the squares of some functional equations. (English) Zbl 1329.39033
Summary: We consider the stability, the superstability and the inverse stability of the functional equations with squares of Cauchy’s, of Jensen’s and of isometry equations and the stability in Ulam-Hyers sense of the alternation of functional equations and of the equation of isometry.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B62 Functional inequalities, including subadditivity, convexity, etc.
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[1] J.A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411-416. Cited on 93. · Zbl 0448.39003
[2] B. Batko, On the stability of an alternative functional equation, Math. Inequal. Appl. 8 (2005), no. 4, 685-691. Cited on 83, 96 and 97. · Zbl 1096.39026
[3] B. Batko, Superstability of the Cauchy equation with squares in finite-dimensional normed algebras, Aequationes Math. 89 (2015), no. 3, 785-789. Cited on 82. · Zbl 1320.39031
[4] P.W. Cholewa, The stability of the sine equation, Proc. Amer. Math. Soc. 88 (1983), no. 4, 631-634. Cited on 93 and 97. · Zbl 0547.39003
[5] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. Cited on 81. · JFM 67.0424.01
[6] D.H. Hyers, S.M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288-292. Cited on 100. · Zbl 0060.26404
[7] M. Kuczma, An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality, Second edition. Birkhäuser Verlag, Basel, 2008. Cited on 87.
[8] Z. Moszner, Sur l’orientation d’un groupe, Tensor (N.S.) 48 (1989), no. 1, 19-20. Cited on 87. · Zbl 0703.20025
[9] Z. Moszner, On stability of some functional equations and topology of their target spaces, Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012), 69-94. Cited on 84 and 86. · Zbl 1292.39027
[10] Z. Moszner, On the inverse stability of functional equations, Banach Center Publications 99 (2013), 111-121. Cited on 98, 99 and 103. · Zbl 1281.39042
[11] M. Omladič, P. Šemrl, On non linear perturbations of isometries, Math. Ann. 303 (1995), no. 1, 617-628. Cited on 100.
[12] W. Żelazko, Algebry Banacha, Biblioteka Matematyczna, Tom 32, PWN,Warsaw, 1968. Cited on 84 and 94.
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