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Probabilistic Normed Groups | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 14، شماره 1، اردیبهشت 2017، صفحه 99-113 اصل مقاله (395.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3045 | ||
| نویسندگان | ||
| Kourosh Nourouzi* 1؛ Alireza Pourmoslemi2 | ||
| 1Faculty of Mathematics, K.N.Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran. | ||
| 2Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran. | ||
| چکیده | ||
| In this paper, we introduce the probabilistic normed groups. Among other results, we investigate the continuity of inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined on probabilistic normed groups and give some results about locally boundedness of such functions. | ||
| کلیدواژهها | ||
| Probabilistic normed groups؛ Invariant probabilistic metrics؛ Distributional-slowly varying functions؛ Midconvex functions | ||
| مراجع | ||
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[1] C. Alsina, B. Schweizer and A. Sklar, On the denition of a probabilistic normed space, Aequationes Math, 46(2) (1993), 91{98. [2] N. H. Bingham and A. J. Ostaszewski, Normed versus topological groups: dichotomy and duality, Dissertationes Math, 472 (2010), 138p. [3] G. Birkho, A note on topological groups, Compositio Math, 3 (1936), 427{430. [4] D. R. Farkas, The algebra of norms and expanding maps on groups, J. Algebra, 133(2) (1990), 386{403. [5] M. Frechet, Sur quelques points du calcul fonctionnel, Rendiconti de Circolo Matematico di Palermo, 22 (1906), 1{74. [6] S. Kakutani, Uber die Metrisation der topologischen Gruppen, (German) Proc. Imp. Acad, 12(4) (1936), 82{84. (also in Selected Papers, Vol. 1, ed. R. Robert Kallman, Birkhuser, (1986), 60{62.) [7] V. L. Klee, Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc, 3 (1952), 484{487. [8] E. Klement, R. Mesiar and E. Pap, Triangular norms, Trends in Logica{Studia Logica Library, Kluwer Academic Publishers, Dordrecht, 8 (2000). [9] M. Kuczma, An introduction to the theory of functional equations and inequalities, Cauchy's equation and Jensen's inequality, Second edition, Birkhauser Verlag, Basel, 2009. [10] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U. S. A, 28 (1942), 535{537. [11] A. A. Pavlov, Normed groups and their application to noncommutative dierential geometry, J. Math. Sci., 113(5) (2003), 675{682. [12] B. J. Pettis, On continuity and openness of homomorphisms in topological groups, Ann. of Math, 52(2) (1950), 293{308. [13] B. Schweizer and A. Sklar, Probabilistic metric spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing Co., New York, 1983. [14] A. N. Serstnev, On the concept of a stochastic normalized space, (Russian), Dokl. Akad. Nauk SSSR, 149 (1963), 280{283. [15] D. A. Sibley, A metric for weak convergence of distribution functions, Rocky Mountain J. Math, 1(3) (1971), 427{430. | ||
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