New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces


Authors

Dingwei Zheng - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China. Zhangyong Cai - Department of Mathematics, Guangxi Teachers Education University, Nanning, Guangxi 530023, P. R. China. Pei Wang - School of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi 537000, P. R. China.


Abstract

In this paper, we introduce the notions of \(\theta-\phi\) contraction and \(\theta-\phi\) Suzuki contraction and establish some new fixed point theorems for these mappings in the setting of complete metric spaces. The results presented in the paper improve and extend the corresponding results due to Banach, Browder [F. E. Browder, Nederl. Akad. Wetensch. Proc. Ser. A Indag. Math., 30 (1968), 27–35], Suzuiki [T. Suzuki, Nonlinear Anal., 71 (2009), 5313–5317], Kannan [R. Kannan, Amer. Math. Monthly, 76 (1969), 405–408], Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages]. Finally, we give an example to illustrate them.


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ISRP Style

Dingwei Zheng, Zhangyong Cai, Pei Wang, New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2662--2670

AMA Style

Zheng Dingwei, Cai Zhangyong, Wang Pei, New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces. J. Nonlinear Sci. Appl. (2017); 10(5):2662--2670

Chicago/Turabian Style

Zheng, Dingwei, Cai, Zhangyong, Wang, Pei. "New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2662--2670


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