Accès libre

Composition iterates, Cauchy, translation, and Sincov inclusions

À propos de cet article

Citez

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

[2] M. Alimohammady, S. Jafari, S. P. Moshokoa and M. K. Kalleji, A note on properties of hypermetric spaces, J. Hyperstructures, 3 (2014), 89–100.Search in Google Scholar

[3] P. Augustová and L. Klapka, Atlas as solutions of Sincov’s inequality, arXiv: 1612.00355v1 [math.DS] 1 Dec 2016, 7 pp.Search in Google Scholar

[4] J. A. Baker, Solution of problem E 2607, Amer. Math. Monthly, 84 (1977), 824–825.10.2307/2322071Search in Google Scholar

[5] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ., 25, Providence, Rhode Island, 1967.Search in Google Scholar

[6] H. Brandt, Über eine Verallgemeinerung der Gruppenbregriffes, Math. Ann., 96 (1926), 360–366.10.1007/BF01209171Search in Google Scholar

[7] M. J. Campión, R. G. Catalán, E. Induráin and G. Ochoa, Reinterpreting a fuzzy subset by means of a Sincov’s functional equation, J. Intelligent Fuzzy Systems, 27 (2014), 367–375.10.3233/IFS-131005Search in Google Scholar

[8] M. J. Campión, E. Induráin, G. Ochoa and O. Valero, Functional equations related to weightable quasi-metrics, Hacet. J. Math. Stat., 44 (2015), 775–787.Search in Google Scholar

[9] M. Cantor, Funktionalgleichungen mit drei von einander unabhängigen Veränderlichen, Zeitschrift Mat. Physik., 41 (1896), 161–163.Search in Google Scholar

[10] E. Castillo-Ron and R. Ruiz-Cobo, Functional Equations in Science and Engineering, Marcel Decker, New York, 1992.Search in Google Scholar

[11] R. Croisot, Une interprétation des relations d’équivalence dans un ensemble, C. R. Acad. Sci. Paris, 226 (1948), 616–617.Search in Google Scholar

[12] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 2002.10.1017/CBO9780511809088Search in Google Scholar

[13] W. Fechner, Richard’s inequality, Cauchy-Schwarz’s inequality and approximate solutions of Sincov’s equation, Proc. Amer. Math. Soc., 147 (2019), 3955–3960.10.1090/proc/14543Search in Google Scholar

[14] W. Fechner, Sincov’s inequalities on topological spaces, Publ. Math. Debrecen, 96 (2020), 63–76.10.5486/PMD.2020.8515Search in Google Scholar

[15] G. Frege, Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen, Dissertation for the Venia docendi, Verlag Friedrich Frommann, Jena, 1874.Search in Google Scholar

[16] G. Frege, Methods of calculation based on an extension of the concept of quantity, In: G. Frege, Collected Papers of on Mathematics, Logic, and Philosophy, Basil Blackwell, Oxford, 1984, 56–92.10.1017/CBO9781139171519.008Search in Google Scholar

[17] Z. Gajda, Invariant means and representations of semigroups in the theory of functional equations, Prace Naukowe Uniwersytetu Śląskiego w Katowicach, 1273 (1992), 1–81.Search in Google Scholar

[18] T. Glavosits, Generated preorders and equivalences, Acta Acad. Paed. Agriensis, Sect. Math., 29 (2002), 95–103.Search in Google Scholar

[19] T. Glavosits and Á. Száz, Constructions and extensions of free and controlled additive relations, In: Th.M. Rassias (Ed.), Handbook of Functional Equations: Functional Inequalities, Springer Optim. Appl. 95 (2014), 161–208.Search in Google Scholar

[20] D. Gronau, Gottlob Frege, a pioneer in iteration theory, In: L. Reich, J. Smítal and Gy. Targonski (Eds.), Proceedings of the European Conference on Iteration Theory, ECIT94, Gracer Math. Ber. 334 (1997), 105–119.Search in Google Scholar

[21] D. Gronau, Gottlob Fregees Beiträge zur Iteratiostheorie und zur Theorie der Functionalgleichungen, In: G. Gabriel (Ed.), Gottlob Frege – Werk und Wirkung, Mentis Verlag, Paderborn, 200, 151–169.10.30965/9783969751800_012Search in Google Scholar

[22] D. Gronau, A remark on Sincov’s functional equation, Notices South African Math. Soc. Esaim: Proceeding and Surveys, 31 (2000), 1–8.Search in Google Scholar

[23] D. Gronau, Translation equation and Sincov’s equation – A historical remark, Esaim: Proceeding and Surveys 46 (2014), 43–46.10.1051/proc/201446004Search in Google Scholar

[24] J. Mala and Á. Száz, Modifications of relators, Acta Math. Hungar., 77 (1997), 69–81.10.1023/A:1006583622770Search in Google Scholar

[25] Z. Moszner, Solution générale de l’équation F(x, y)F(y, z)= F(x, z) pour x y z, C. R. Acad. Sci. Paris, 261 (1965), 28.Search in Google Scholar

[26] Z. Moszner, L’équation de translation et l1équation de Sincov généralisée, Rocznik Nauk.-Dydakt. Prace Mat., 16 (1999), 53–71.Search in Google Scholar

[27] Z. Moszner, On the stability of functional equations, Aequationes Math., 77 (2009), 33–88.10.1007/s00010-008-2945-7Search in Google Scholar

[28] K. Nikodem, Additive selections of additive set-valued functions, Zb. Rad. Prirod.-Mat. Fak., 18 (1988), 143–148.Search in Google Scholar

[29] K. Nikodem and D. Popa, On single-valuedness of set-valued maps satisfying linear inclusions, Banach J. Math. Anal., 3 (2009), 44–51.10.15352/bjma/1240336422Search in Google Scholar

[30] G. Pataki and Á. Száz, A unified treatment of well-chainedness and connectedness properties, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 19 (2003), 101–165.Search in Google Scholar

[31] J. Pepis, Sur une famille d’ensembles plans et les solutions de l’équation fonctionnelle F(x, z)= F(x, y) · F(y, z) pour 0 x y z. Applicationá la théorie générale des intéréts, Ann. Soc. Polon. Math., 17 (1937), 113.Search in Google Scholar

[32] W. J. Pervin, Quasi-uniformization of topological spaces, Math. Ann., 147 (1962), 316–317.10.1007/BF01440953Search in Google Scholar

[33] B. Piatek, On the Sincov functional equation, Demonstratio Math., 38 (2005), 875–881.10.1515/dema-2005-0411Search in Google Scholar

[34] P. K. Sahoo, Stability of a Sincov type functional equation, J. Inf. Math. Sci., 1 (2009), 81–90.Search in Google Scholar

[35] P. K. Sahoo, On a Sincov type functional equation, In: Th.M. Rassias and J. Brzdek (Eds.), Functional Equations in Mathematical Analysis, Springer Optimizations and Its Applications, 52, Chapter 43, Springer, New York, 2012, 697–7008.10.1007/978-1-4614-0055-4_43Search in Google Scholar

[36] D. M. Sincov, Über eine Funktionalgleichung, Arch. Math. Phys., 6 (1904), 216–217.Search in Google Scholar

[37] A. Smajdor, Iterations of multi-valued functions, Prace Naukowe Universytetu Ślaskiego w Katowicach 759, Universitet Ślaski, Katowice 1985.Search in Google Scholar

[38] W. Smajdor, Set-valued version of Sincov’s functional equation, Demonstration Math., 39 (2006), 101–105.10.1515/dema-2006-0114Search in Google Scholar

[39]Á. Száz, Galois type connections and closure operations on preordered sets, Acta Math. Univ.Comen., 78 (2009), 1–21.Search in Google Scholar

[40]Á. Száz, Corelations are more powerful tools than relations, In: Th.M. Rassias (Ed.), Applications of Nonlinear Analysis, Springer Optimization and Its Applications, 134 (2018), 711–779.10.1007/978-3-319-89815-5_25Search in Google Scholar

[41] A. Weil, Sur les espacesá structure uniforme at sur la topologie générale, Actual. Sci. Ind., 551 Herman and Cie, Paris, 1937.Search in Google Scholar

eISSN:
2066-7752
Langue:
Anglais
Périodicité:
2 fois par an
Sujets de la revue:
Mathematics, General Mathematics