Weak \(\theta-\phi-\)contraction and discontinuity

Volume 10, Issue 5, pp 2318--2323 http://dx.doi.org/10.22436/jnsa.010.05.04

Publication Date: May 22, 2017 Submission Date: July 21, 2016

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Authors

Dingwei Zheng - College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, 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 notion of weak \(\theta-\phi-\)contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233–245].

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ISRP Style

Dingwei Zheng, Pei Wang, Weak \(\theta-\phi-\)contraction and discontinuity, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2318--2323

AMA Style

Zheng Dingwei, Wang Pei, Weak \(\theta-\phi-\)contraction and discontinuity. J. Nonlinear Sci. Appl. (2017); 10(5):2318--2323

Chicago/Turabian Style

Zheng, Dingwei, Wang, Pei. "Weak \(\theta-\phi-\)contraction and discontinuity." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2318--2323

Keywords

Fixed point
discontinuity
weak \(\theta-\phi-\)contraction.

MSC

47H10
54H25

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