# Fixed point theorems for improved $\alpha$-Geraghty contractions in partial metric spaces

Volume 9, Issue 6, pp 4436--4449
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### Authors

Muhammad Nazam - Department of Mathematics and Statistics, International Islamic University, H-10 Islamabad, Pakistan. Muhammad Arshad - Department of Mathematics and Statistics, International Islamic University, H-10 Islamabad, Pakistan. Choonkil Park - Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea.

### Abstract

Rosa and Vetro [V. La Rosa, P. Vetro, J. Nonlinear Sci. Appl., 7 (2014), 1-10] established new fixed point results in complete partial metric spaces. In this paper, we improve the notion of $\alpha$-Geraghty contraction type mappings and establish some common fixed point theorems for a pair of $\alpha$-admissible mappings under an improved notion of $\alpha$-Geraghty contraction type mappings in complete partial metric spaces. We give an example to illustrate these results. An application of main result to the existence of solution of system of integral equations is also presented.

### Share and Cite

##### ISRP Style

Muhammad Nazam, Muhammad Arshad, Choonkil Park, Fixed point theorems for improved $\alpha$-Geraghty contractions in partial metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4436--4449

##### AMA Style

Nazam Muhammad, Arshad Muhammad, Park Choonkil, Fixed point theorems for improved $\alpha$-Geraghty contractions in partial metric spaces. J. Nonlinear Sci. Appl. (2016); 9(6):4436--4449

##### Chicago/Turabian Style

Nazam, Muhammad, Arshad, Muhammad, Park, Choonkil. "Fixed point theorems for improved $\alpha$-Geraghty contractions in partial metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4436--4449

### Keywords

• Fixed point
• $\alpha$-Geraghty contraction
• partial metric space.

•  47H09
•  54H25
•  47H10

### References

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