Ulam stability for Thunsdorff and Cauchy-Schwarz equations

.blurhash-client-img { display: none !important; }

Open Access

|Dec 2020

Abstract

We consider the equality case in Thunsdorff inequality and Cauchy-Schwarz inequality. For these two equations we prove Ulam stability.

[1] H. Alzer, On an integral inequality for concave functions, Acta. Sci. Math., vol. 56, 1992, 79-82.
Search in Google Scholar Back to article
[2] S. Barza, C. P. Niculescu, Integral equations for concave functions, Publ. Math. Debrecen, vol. 68, 2006, 139-159.10.5486/PMD.2006.3197
Search in Google Scholar Back to article
[3] J. Brzdek, D. Popa, I. Raşa, B. Xu, Ulam stability of Operators, Academic Press, Elsevier, 2018.
Search in Google Scholar Back to article
[4] A. M. Fink, M. Jodeit Jr., Jensen inequalities for functions with monotonicities, Aeq. Mathematicae, vol. 40, 1990, 26-43.10.1007/BF02112278
Search in Google Scholar Back to article
[5] M. Petschke, Extremalstrahlen konvexer Kegel un komplementäre Ungleichungen, Dissertation Darmstadt, 1989.
Search in Google Scholar Back to article
[6] D. Popa, I. Raşa, Best constant in Hyers-Ulam stability of some functional equations, Carpathian J. Math., vol. 30, 2014, 383-386.10.37193/CJM.2014.03.04
Search in Google Scholar Back to article
[7] I. Raşa, T. Vladislav, Inegalităţi şi aplicaţii, Editura Tehnică, Bucureşti, 2000.
Search in Google Scholar Back to article
[8] L. Stanković, Extentions of Thunsdorff ’s inequality to the case of convex functions of order k, Univ. Beograd, Publ. Elektrotehn. Fak. Mat. Fiz., no. 498-541, 1975, 145-148.
Search in Google Scholar Back to article
[9] H. Thunsdorff, Konvex Funktionen und Ungleichungen, Univ. of Göttingen, 1932.
Search in Google Scholar Back to article