# Fixed point belonging to the zero-set of a given function

Volume 11, Issue 3, pp 417--424
Publication Date: February 22, 2018 Submission Date: October 30, 2017 Revision Date: December 28, 2017 Accteptance Date: December 31, 2017
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### Authors

Francesca Vetro - Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam. - Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam.

### Abstract

We prove the existence and uniqueness of fixed point belonging to the zero-set of a given function. The results are established in the setting of metric spaces and partial metric spaces. Our approach combines the recent notions of $(F,\varphi)$-contraction and $\mathcal{Z}$-contraction. The main result allows to deduce, as a particular case, some of the most known results in the literature. An example supports the theory.

### Share and Cite

##### ISRP Style

Francesca Vetro, Fixed point belonging to the zero-set of a given function, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 3, 417--424

##### AMA Style

Vetro Francesca, Fixed point belonging to the zero-set of a given function. J. Nonlinear Sci. Appl. (2018); 11(3):417--424

##### Chicago/Turabian Style

Vetro, Francesca. "Fixed point belonging to the zero-set of a given function." Journal of Nonlinear Sciences and Applications, 11, no. 3 (2018): 417--424

### Keywords

• Fixed point
• metric space
• partial metric space
• nonlinear contraction
• simulation function

•  47H10
•  54H25

### References

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