Generalization of the Harmonic Weighted Mean Via Pythagorean Invariance Identity and Application

[1] J. Aczél, Lectures on Functional Equations and Their Applications, Mathematics in Science and Engineering, 19, Academic Press, New York, 1966.Search in Google Scholar

[2] P.S. Bullen, Handbook of Means and Their Inequalities, Mathematics and its Applications, 560, Kluwer Academic Publishers Group, Dordrecht, 2003.10.1007/978-94-017-0399-4Search in Google Scholar

[3] P. Kahlig and J. Matkowski, On the composition of homogeneous quasi-arithmetic means, J. Math. Anal. Appl. 216 (1997), 69–85.10.1006/jmaa.1997.5648Search in Google Scholar

[4] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Państwowe Wydawnictwo Naukowe and Uniwersytet Śląski, Warszawa–Kraków–Katowice, 1985; Second edition, edited and with a preface by A. Gilányi, Birkhäuser Verlag, Basel, 2009.10.1007/978-3-7643-8749-5Search in Google Scholar

[5] J. Matkowski, Invariant and complementary quasi-arithmetic means, Aequationes Math. 57 (1999), 87–107.10.1007/s000100050072Search in Google Scholar

[6] J. Matkowski, Iterations of mean-type mappings and invariant means, Ann. Math. Sil. 13 (1999), 211–226.Search in Google Scholar

[7] J. Matkowski, Iterations of the mean-type mappings, in: A.N. Sharkovsky and I.M. Sushko (eds.), Iteration Theory (ECIT’08), Grazer Mathematische Berichte, 354, Karl-Franzens-Universität Graz, Graz, 2009, pp. 158–179.Search in Google Scholar

[8] J. Matkowski, Generalized weighted arithmetic means, in: Th.M. Rassias and J. Brzdęk (eds.), Functional Equations in Mathematical Analysis, Springer, New York, 2012, pp. 563–582.10.1007/978-1-4614-0055-4_36Search in Google Scholar

[9] J.S. Ume and Y.H. Kim, Some mean values related to the quasi-arithmetic mean, J. Math. Anal. Appl. 252 (2000), 167–176.10.1006/jmaa.2000.6963Search in Google Scholar