# Fixed point theorems for partial $\alpha-\psi$ contractive mappings in generalized metric spaces

Volume 9, Issue 1, pp 83--91
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### Authors

Aphinat Ninsri - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand. Wutiphol Sintunavarat - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand.

### Abstract

In this paper, we introduce the concept of partial $\alpha-\psi$ contractive mappings along with generalized metric distance. We also establish the existence of fixed point theorems for such mappings in generalized metric spaces. Our results extend and unify main results of Karapinar [E. Karapinar, Abstr. Appl. Anal., 2014 (2014), 7 pages] and several well-known results in literature. We give some examples to illustrate the usability of our results. Moreover, we prove the fixed point results in generalized metric space endowed with an arbitrary binary relation and the fixed point results in generalized metric space endowed with graph.

### Share and Cite

##### ISRP Style

Aphinat Ninsri, Wutiphol Sintunavarat, Fixed point theorems for partial $\alpha-\psi$ contractive mappings in generalized metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 83--91

##### AMA Style

Ninsri Aphinat, Sintunavarat Wutiphol, Fixed point theorems for partial $\alpha-\psi$ contractive mappings in generalized metric spaces. J. Nonlinear Sci. Appl. (2016); 9(1):83--91

##### Chicago/Turabian Style

Ninsri, Aphinat, Sintunavarat, Wutiphol. "Fixed point theorems for partial $\alpha-\psi$ contractive mappings in generalized metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 83--91

### Keywords

• Fixed point theory
• partial $\alpha-\psi$ contractive mappings
• generalized metric spaces
• binary relation.

•  47H10
•  54H25

### References

• [1] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37.

• [2] E. Karapinar , Discussion on $\alpha-\psi$ contractions on generalized metric spaces, Abstr. Appl. Anal., 2014 (2014), 7 pages.

• [3] W. A. Kirk, N. Shahzad , Generalized metrics and Caristis theorem, Fixed Point Theory Appl., 2013 (2013), 9 pages.

• [4] I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca (2001)

• [5] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for $\alpha-\psi$ -contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.