Classes of Linear Operators in Probabilistic Normed Space

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Iqbal Hamzh Jebril
Mohd. Salmi MD. Noorani

Abstract

In this paper we will introduce the classes of linear operators in probabilistic normed space, as the set of all Certainly bounded Lc(V,V’), D-bounded LD(V,V’), strongly B-bounded LB(V,V’), and strongly ѱ – bounded Lѱ(V,V’), we then prove they are linear space.


Keywords: Linear operators, Probabilistic Normed Space


Corresponding author: E-mail: [email protected]


 

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Original Research Articles

References

[1] Alsina, C., Schweizer, B. and Sklar, A, 1997. Continuity properties of probabilistic norms, Journal of Mathematical Analysis and Applications, Vol. 208, pp: 446-452.
[2] Alsina, C., Schweizer, B. and Sklar, A, 1993. On the definition of probabilistic normed space, Aequation Mathematicae, vol.46, pp: 91-98.
[3] Jebril, I. and Ali, R, 2003. Bounded linear operators in probabilistic normed space, J. Inequal. Pure and Appl. Math., Vol. 4, Issue 1, Article 8.
[4] Jebril, I. and Noorani, M. S. 2004, Contraction functions in probabilistic normed space, J. of Inst. Of Math. & Comp. Sci. (accepted)
[5] Kreyszig, E, 1978. Introductory functional analysis with applications, John Wiley and Sons Inc. New York.
[6] Lafuerza Guillen, B., Rodriguez Lallena J.A. and Sempi, C, 1999. A study of boundedness in probabilistic normed spaces, Journal of Mathematical Analysis and Applications, Vol. 232, pp: 183-196.
[7] Lafuerza Guillen, B., Rodriguez Lallena J.A. and Sempi, C, 1995. Completion of probabilistic normed spaces, Internat. J. Math. Math. Sci. 18, pp: 649-652.
[8] Lafuerza Guillen, B., Rodriguez Lallena J.A. and Sempi, C, 1998. Probabilistic norms for linear operators, Journal of Mathematical Analysis and Applications, Vol. 220, pp: 462-476.
[9] Schweizer, B. and Sklar, A., 1983. Probabilistic metric space. Elsevier North Holland New York.,