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Title

Probabilistic Metric Spaces and Some Contraction Mappings

Author

Parvin Azhdari

Citation 
Vol. 17 No. 2 pp. 5660

Abstract

There exist many types of contraction mappings in the case of single valued and multi valued that researchers are interested in proving fixed point theorems. Now, I consider two types of contraction: (¥õ ? k) ? B contraction and bncontraction . In this paper, after presenting the definition of (¥õ ? k) ? B contraction, I prove a lemma about continuity of (¥õ ? k) ? B contraction and by using it I prove a unique single valued fixed point theorem for (¥õ ? k) ? B contraction with tnorm which is ¥õconvergent in probabilistic metric space. Then multivalued bncontraction definition is illustrated. I obtain first multivalued theorem with new assumptions. Finally, I prove another fixed point theorem for multivalued case by the definition of a large class of mappings called weakly demicompact mappings.

Keywords

Probabilistic metric space, bncontraction, (¥õ ? k) ? B contraction, fixed point.

URL

http://paper.ijcsns.org/07_book/201702/20170207.pdf

