Geodesic
Weak $\theta-\phi-$contraction and discontinuity
Zheng, Dingwei1 ; Wang, Pei2
1 College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China
2 School of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi 537000, P. R. China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 5, p. 2318-2323.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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].
DOI : 10.22436/jnsa.010.05.04
Classification : 47H10, 54H25
Keywords: Fixed point, discontinuity, weak \(\theta-\phi-\)contraction.

Zheng, Dingwei 1 ; Wang, Pei 2

1 College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, P. R. China
2 School of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi 537000, P. R. China 
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Zheng, Dingwei; Wang, Pei. Weak \(\theta-\phi-\)contraction and discontinuity. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 5, p. 2318-2323. doi : 10.22436/jnsa.010.05.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.05.04/

[1] Bisht, R. K.; Pant, R. P. A remark on discontinuity at fixed point, J. Math. Anal. Appl., Volume 445 (2017), pp. 1239-1241 | Zbl | DOI

[2] Bojor, F. Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., Volume 75 (2012), pp. 3895-3901 | DOI

[3] Ćirić, L.; Abbas, M.; Saadati, R.; Hussain, N. Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., Volume 217 (2011), pp. 5784-5789 | DOI

[4] Jleli, M.; Samet, B. A new generalization of the Banach contraction principle, J. Inequal. Appl., Volume 2014 (2014), pp. 1-8 | DOI

[5] Kannan, R. Some results on fixed points, II, Amer. Math. Monthly, Volume 76 (1969), pp. 405-408

[6] Pant, R. P. Discontinuity and fixed points, J. Math. Anal. Appl., Volume 240 (1999), pp. 284-289 | DOI

[7] Piri, H.; Kumam, P. Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-11 | DOI | Zbl

[8] Ran, A. C. M.; Reurings, M. C. B. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., Volume 132 (2003), pp. 1435-1443 | Zbl | DOI

[9] Rhoades, B. E. A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., Volume 226 (1977), pp. 257-290 | Zbl | DOI

[10] Rhoades, B. E. Contractive definitions and continuity, Fixed point theory and its applications, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, Volume 72 (1988), pp. 233-245 | DOI

[11] Hierro, A. F. Roldán-López de; Shahzad, N. New fixed point theorem under R-contractions, Fixed Point Theory Appl., Volume 2015 (2015), pp. 1-18 | Zbl | DOI

[12] Samet, B.; Vetro, C.; Vetro, P. Fixed point theorems for \(\alpha\psi\) -contractive type mappings, Nonlinear Anal., Volume 75 (2012), pp. 2154-2165 | DOI

[13] Suzuki, T. A new type of fixed point theorem in metric spaces, Nonlinear Anal., Volume 71 (2009), pp. 5313-5317 | DOI

[14] Wardowski, D. Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-6 | DOI

[15] Zheng, D.-W.; Cai, Z.-Y.; Wang, P. New fixed point theorems for \(\theta-\phi-\)contraction in complete metric spaces (Preprint) | DOI

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