Classes of Linear Operators in Probabilistic Normed Space
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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: Iqbal501@yahoo.com
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References
[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.,