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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.33 no.4 Antofagasta Dec. 2014 

Fróchet differentiation between Menger probabilistic normed spaces

N. Eghbali

University of Mohaghegh Ardabili



In this paper, we define and study Menger weakly and strongly P-convergent sequences and then Menger probabilistic continuity. We also display Frechet differentiation of nonlinear operators between Menger probabilistic normed spaces.

Subjclass : 46S40.

Keywords : Menger probabilistic normed spaces; Frehet differentiation; nonlinear operators.


[1] C. Alsina, B. Schweizer and A. Sklar, On the definition of a probabilistic normed space, Aequationes Math. 46, pp. 91—98, (1993).         [ Links ]

[2] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, Thejournal of Fuzzy Mathematics, 11, pp. 687—705, (2003).         [ Links ]

[3] B. Buffoni and J. Toland, Analytic theory of global bifurcation, Princeton Oxford: Princeton University Press; (2003).         [ Links ]

[4] S.S.Chang, Y. J.Cho andS.M. Kang, Probabilistic metric spaces and nonlinear operator theory, Sichuan University Press, Chengdu,(1994).         [ Links ]

[5] M.S.ElNaschie, On the uncertainly of Cantorian geometry and two-slit experiment, Choas, Solitions and Fractals, 9, pp. 517—529, (1998).

[6] M.S. ElNaschie, On the unification of heterotic strings, M theory and å°° theory, Choas, Solitions and Fractals, 11, pp. 2397—2408, (2000).

[7] K. Mengar, Statistical metrics, Proc. Nat. Acad. Sci. 28, pp. 535—537,(1942).         [ Links ]

[8] M. Mursaleen and Q. M. Danish Lohani, Statistical limit superior and limit inferior in probabilistic normed spaces,Filomat,25(3),pp.55-67, (2011).         [ Links ]

[9] M. Mursaleen and S. A. Mohiuddine, On ideal convergence ofdouble sequences in probabilistic normed spaces, Math. Reports, 12 (64) (4),pp. 359-371, (2010).         [ Links ]

[10] M. Mursaleen and S. A. Mohiuddine, Nonlinear operators between intuituinistic fuzzy normed spaces and Frechet derivative, Chaos, solitions and Fractals, 42 (2), pp. 1010—1015, (2009).         [ Links ]

[11] A. N. Serstnev, On the notion of a random normed space, Dokl. Akad. Nauk. 149, pp. 280—283, (1963).         [ Links ]

N. Eghbali

Department of Mathematics and Applications

Faculty of Mathematical Sciences

University of Mohaghegh Ardabili




e-mail :

Received : May 2014. Accepted : August 2014

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