To search, Click below search items.

 

All Published Papers Search Service

Title

Probabilistic Metric Spaces and Some Contraction Mappings

Author

Parvin Azhdari

Citation

Vol. 17  No. 2  pp. 56-60

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: (φ ? k) ? B contraction and bn-contraction . In this paper, after presenting the definition of (φ ? k) ? B contraction, I prove a lemma about continuity of (φ ? k) ? B contraction and by using it I prove a unique single valued fixed point theorem for (φ ? k) ? B contraction with t-norm which is φ-convergent in probabilistic metric space. Then multi-valued bn-contraction definition is illustrated. I obtain first multi-valued theorem with new assumptions. Finally, I prove another fixed point theorem for multi-valued case by the definition of a large class of mappings called weakly demicompact mappings.

Keywords

Probabilistic metric space, bn-contraction, (φ ? k) ? B contraction, fixed point.

URL

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