Cyclic quasi-contractions of Ćirić type in b-metric spaces

Volume 10, Issue 3, pp 1075--1088 http://dx.doi.org/10.22436/jnsa.010.03.18

Publication Date: March 20, 2017 Submission Date: June 29, 2016

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Authors

Fei He - School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China. Xiao-Yue Zhao - School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China. Yu-Qi Sun - School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.

Abstract

In this paper, we give a negative answer to the open question raised by Radenovic et al. [S. Radenović, T. Došenović, T. A. Lampert, Z. Golubović, Appl. Math. Comput., 273 (2016), 155–164]. Namely, we give two examples which show that the set of fixed points for cyclic quasi-contractive mappings of Ćirić type may be empty. Then, by using a new lemma, we give some sufficient conditions for the existence of fixed point for cyclic and non-cyclic quasi-contractive mappings of Ćirić type in b-metric spaces. In particular, we show that the condition of Fatou property in the result of Amini-Harandi [A. Amini-Harandi, Fixed Point Theory, 15 (2014), 351–358] may be omitted.

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ISRP Style

Fei He, Xiao-Yue Zhao, Yu-Qi Sun, Cyclic quasi-contractions of Ćirić type in b-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1075--1088

AMA Style

He Fei, Zhao Xiao-Yue, Sun Yu-Qi, Cyclic quasi-contractions of Ćirić type in b-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(3):1075--1088

Chicago/Turabian Style

He, Fei, Zhao, Xiao-Yue, Sun, Yu-Qi. "Cyclic quasi-contractions of Ćirić type in b-metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1075--1088

Keywords

b-metric space
fixed point
cyclic quasi-contractions of Ćirić type
Fatou property.

MSC

47H10
54H25

References

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