Fréchet differentiation between Menger probabilistic normed spaces
DOI:
https://doi.org/10.4067/S0716-09172014000400005Keywords:
Menger probabilistic normed spaces, Frechet differentiation, nonlinear operators, espacios probabilísticos normados de Menger, diferenciación de Frechet, operadores no-lineales.Abstract
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.References
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[2] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, The journal of Fuzzy Mathematics, 11, pp. 687—705, (2003).
[3] B. Buffoni and J. Toland, Analytic theory of global bifurcation, Princeton Oxford: Princeton University Press; (2003).
[4] S. S. Chang, Y. J. Cho and S. M. Kang, Probabilistic metric spaces and nonlinear operator theory, Sichuan University Press, Chengdu, (1994).
[5] M. S. El Naschie, On the uncertainly of Cantorian geometry and twoslit experiment, Choas, Solitions and Fractals, 9, pp. 517—529, (1998).
[6] M. S. El Naschie, 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).
[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).
[9] M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12 (64) (4), pp. 359-371, (2010).
[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).
[11] A. N. Serstnev, On the notion of a random normed space, Dokl. Akad. Nauk. 149, pp. 280—283, (1963).
Published
2017-03-23
How to Cite
[1]
N. Eghbali, “Fréchet differentiation between Menger probabilistic normed spaces”, Proyecciones (Antofagasta, On line), vol. 33, no. 4, pp. 415-435, Mar. 2017.
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