Author, Subjects, Keywords

Cited Author

 
 
   » By Author or Editor
 » Browse Author by Alphabet
 » By Journal
 » By Subjects
 » Malaysian Journals
 » By Type
 » By Year
 » By Latest Additions
 
 
   » By Author
 » Top 20 Authors
 » Top 20 Article
 » Top Journal Cited
 » Top Article Cited
 » Journal Citation Statistics
 » Usage Since Sept 2007


 
 
 

Login | Create Account

Strongly ψ-Bounded and Classes of Linear Operators in Probabilistic Normed Space

Jebril, I.H., and Mohd. Salmi Md. Noorani , (2005) Strongly ψ-Bounded and Classes of Linear Operators in Probabilistic Normed Space. Bulletin of the Malaysian Mathematical Sciences Society, 28 (2). pp. 173-182. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v28n2/v28n2p8.pdf

Affiliations

Universiti Kebangsaan Malaysia, School of Mathematical Sciences.

Abstract

In this paper we redefined the definition of a bounded linear operator in probabilistic normed space by introducing the notion of strongly $\psi$-bounded linear maps. We then show that this new definition of boundedness implies all contraction functions in probabilistic normed space are bounded. Also, we introduce the classes of linear operators in probabilistic normed space, as the set of all certainly bounded $L_c (V,V')$, $D$-bounded $L_D (V,V')$, strongly $B$-bounded $L_B (V,V')$, and strongly $\psi$-bounded $L_\psi (V,V')$ we then prove they are linear spaces.

Item Type:Journal
Keywords:linear operators, probalistic normed space.
Subjects:Q Science, Computer Science
ID Code:1421

[1] C. Alsina, B. Schweizer, and A. Sklar, Continuity properties of probabilistic norms, J. Math. Anal. Appl. 208 (1997), 446—452.

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

[3] 0. Hadzic and E. Pap, A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Set and Systems, 127 (2002), 333—344.

[4] 0. Hadzic, Fixed point theory in probabilistic metric spaces, Univ. Novi Sad, Novi Sad, 1995.

[5] 0. Hadzic and E. Pap, A Fixed Point Theorem in PM Spaces, Kluwer Acad. Publ., Dordrecht, 2001.

[6] Jebril, I.H. and R.I. Ali, Bounded linear operators in probabilistic normed space, J. Inequal. Pure Appl. Math. 4(1) (2003), 7.

[7] B. Lafuerza Guillén, J. A. Rodrigues Lallena and C. Sempi, A study of boundedness in probabilistic normed spaces, J. Math. Anal. Appl. 232 (1999), 183—196

[8] B. Lafuerza Guillén, J. A. Rodrigues Lallena and C. Sempi, Completion of probabilistic normed spaces, Internat. J. Math. Math. Sci. 18 (1995), 649—652.

[9] D. Mihet, A fixed point theorem for weak-Hicks contractions, Seminar of Probability Theory and Applications, 135, 2002.

[10] D. Mihet, A subclass of B-contractions, Seminar of Probability Theory and Applications, 127, 2002.

[11] V. Radu, A fixed point theorem for probabilistic contractions on fuzzy Menger spaces, The 14th European Conference on Iteration Theory (ECIT 2002) Evora, Portugal, September 1-7, 2002.

[12] V. Radu, Some remarks on the probabilistic contractions on Menger spaces, The 8th International Conference on Applied Mathematics and Computer Science, Cluj-Napoca, 2002.

[13] B. Schweizer and A. Sklar, Probabilistic Metric Space, Elsevier North Holland, New York, 1983.

Repository Staff Only: item control page
 
 
 
 
 
 
© Copyright 2007 MyAIS Faculty of Computer Science and Information Technology, University of Malaya – All Rights Reserved. Malaysian Abstracting and Indexing System is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.