# Generalization of Khan fixed point theorem

Volume 17, Issue 1, pp 76--83
Publication Date: March 15, 2017 Submission Date: April 22, 2016
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### Authors

Hossein Piri - Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, 5551761167, Iran. Samira Rahrovi - Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, 5551761167, Iran. Poom Kumam - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan.

### Abstract

In this paper, we study some results of existence and uniqueness of fixed points for a class of mappings satisfying an inequality of rational expressions. Our main result extends and unifies the well-known results of Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste, 8 (1976), 69–72].

### Share and Cite

##### ISRP Style

Hossein Piri, Samira Rahrovi, Poom Kumam, Generalization of Khan fixed point theorem, Journal of Mathematics and Computer Science, 17 (2017), no. 1, 76--83

##### AMA Style

Piri Hossein, Rahrovi Samira, Kumam Poom, Generalization of Khan fixed point theorem. J Math Comput SCI-JM. (2017); 17(1):76--83

##### Chicago/Turabian Style

Piri, Hossein, Rahrovi, Samira, Kumam, Poom. "Generalization of Khan fixed point theorem." Journal of Mathematics and Computer Science, 17, no. 1 (2017): 76--83

### Keywords

• Fixed point
• metric space
• Khan theorem.

•  74H10
•  54H25

### References

• [1] B. Fisher, On a theorem of Khan, Riv. Math. Univ. Parma., 4 (1978), 135–137.

• [2] M. S. Khan, A fixed point theorem for metric spaces, Rend. Inst. Math. Univ. Trieste, 8 (1976), 69–72.

• [3] N. Redjel, A. Dehici, E. Karapinar, I. M. Erhan, Fixed point theorems for ($alpha, psi$)-Meir-Keeler-Khan mappings, J. Nonlinear Sci. Appl., 8 (2015), 955–964.

• [4] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683–2693.