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Some Common Fixed Point Theorems in Probabilistic Metric Space using Contractive Condition of Integral Type


Affiliations
1 D. S. M. College, Jintur, Dist. Parbhani, Maharashtra 431 509, India
2 S. G. R. G. Shinde Mahavidyalaya, Paranda, Dist. Osmanabad, Maharashtra 413 502, India
     

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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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  • Some Common Fixed Point Theorems in Probabilistic Metric Space using Contractive Condition of Integral Type

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Authors

U. P. Dolhare
D. S. M. College, Jintur, Dist. Parbhani, Maharashtra 431 509, India
V. V. Nalawade
S. G. R. G. Shinde Mahavidyalaya, Paranda, Dist. Osmanabad, Maharashtra 413 502, India

Abstract


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.


References