# Journal of the Ramanujan Mathematical Society

Volume 34, Issue 1, March 2019 pp. 81–95.

Some common fixed point theorems in probabilistic metric space using contractive condition of integral type

**Authors**:
U. P. Dolhare and V. V. Nalawade

**Author institution:**D. S. M. College, Jintur, Dist. Parbhani, Maharashtra 431 509, India

**Summary: **
The following notions related to probabilistic metric spaces have
been mentioned in the first section of this research article.
(1) Commuting Self Maps,
(2) Weakly Commuting Self Maps,
(3) Compatible Self Maps,
(4) Weakly Compatible Self Maps,
(5) Occasionally Weakly Compatible Self Maps.
While mentioning the above stated concepts, it has been also
proved that each pair of self maps satisfies the conditions of its
successor, but none of the reverse implication is true. Examples
are provided to illustrate these ideas. In the main results, some
common fixed point theorems using contractive conditions of
integral type in the probabilistic metric spaces are established.
An example is presented to validate the results.

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