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Title |
Probabilistic Metric Spaces and Some Contraction Mappings |
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Author |
Parvin Azhdari |
| Citation |
Vol. 17 No. 2 pp. 56-60 |
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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. |
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Keywords |
Probabilistic metric space, bn-contraction, (φ ? k) ? B contraction, fixed point. |
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