Geodesic
Some fixed point theorems for $\theta$-$\phi$ ${C}$-contractions
Zheng, Dingwei 1 ; Liu, Xinhe 1 ; Zhang, Gengrong 2
1 College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China
2 College of Mathematics and Computationl Science, Hunan First Normal University, Changsha, Hunan, 410205, P. R. China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5723-5733.

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

In this paper, we introduce the notion of $\theta$-$\phi$ ${C}$-contraction and establish some fixed point and coupled fixed point theorems for these mappings in the setting of complete metric spaces and ordered metric spaces. The results presented in the paper improve and extend some well-known results. Also, we give an example to illustrate them.
DOI : 10.22436/jnsa.010.11.10
Classification : 47H10, 54H25
Keywords: Fixed point, coupled fixed point, complete metric space, \(\theta\)-\(\phi\) \({C}\)-contraction

Zheng, Dingwei  1 ; Liu, Xinhe  1 ; Zhang, Gengrong  2

1 College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P. R. China
2 College of Mathematics and Computationl Science, Hunan First Normal University, Changsha, Hunan, 410205, P. R. China 
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Zheng, Dingwei ; Liu, Xinhe ; Zhang, Gengrong . Some fixed point theorems for \(\theta\)-\(\phi\) \({C}\)-contractions. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5723-5733. doi : 10.22436/jnsa.010.11.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.11.10/

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

[2] Boyd, D. W.; Wong, J. S. W. On nonlinear contractions, Proc. Amer. Math. Soc., Volume 20 (1969), pp. 458-464

[3] F. E. Browder On the convergence of successive approximations for nonlinear functional equations, Indag. Math., Volume 71 (1968), pp. 27-35

[4] Chatterjea, S. K. Fixed-point theorems , C. R. Acad. Bulgare Sci., Volume 25 (1972), pp. 727-730

[5] B. S. Choudhury Unique fixed point theorem for weakly C-contractive mappings, Kathmandu Univ. J. Sci. Eng. Technol., Volume 5 (2009), pp. 6-13

[6] Choudhury, B. S.; Kundu, A. A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., Volume 73 (2010), pp. 2524-2531 | DOI

[7] Dugundji, J.; Granas, A. Weakly contractive maps and elementary domain invariance theorem, Bull. Soc. Math. Gréce (N.S.), Volume 19 (1978), pp. 141-151 | Zbl

[8] Fadail, Z. M.; Ahmad, A. G. B.; Rad, G. S.; Ozturk, V.; S. Radenović Some remarks on coupled, tripled and n-tupled coincidence and fixed points theorems in ordered abstract metric spaces, Far East J. Math. Sci., Volume 97 (2015), pp. 809-839 | DOI | Zbl

[9] Bhaskar, T. Gnana; V. Lakshmikantham Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., Volume 65 (2006), pp. 1379-1393 | DOI

[10] Harjani, J.; López, B.; K. Sadarangani Fixed point theorems for weakly C-contractive mappings in ordered metric spaces, Comput. Math. Appl., Volume 61 (2011), pp. 790-796 | DOI

[11] J. R. Jachymski Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., Volume 125 (1997), pp. 2327-2335 | Zbl | DOI

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

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

[14] Matkowski, J. Integrable solutions of functional equations, Dissertationes Math. (Rozprawy Mat.), Volume 127 (1975), pp. 1-68 | EuDML

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

[16] S. Radenović Remarks on some coupled fixed point results in partial metric spaces, Nonlinear Funct. Anal. Appl., Volume 18 (2013), pp. 39-50 | Zbl

[17] Radenović, S. A note on tripled coincidence and tripled common fixed point theorems in partially ordered metric spaces, Appl. Math. Comput., Volume 236 (2014), pp. 367-372 | DOI | Zbl

[18] Radenović, S. Bhaskar-Lakshmikantham type results for monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., Volume 5 (2014), pp. 96-103 | Zbl

[19] Radenović, S. Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math., Volume 38 (2014), pp. 249-257 | DOI

[20] Radenović, S. Remarks on some coupled coincidence point results in partially ordered metric spaces, Arab J. Math. Sci., Volume 20 (2014), pp. 29-39 | DOI | Zbl

[21] B. Samet Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., Volume 72 (2010), pp. 4508-4517 | DOI | Zbl

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

[23] Shatanawi, W. Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Modelling, Volume 54 (2011), pp. 2816-2826 | DOI

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

[25] Zheng, D.-W.; Cai, Z.-Y.; P. Wang New fixed point theorems for \(\theta-\phi\) contraction in complete metric spaces, J. Nonlinear Sci. Appl., Volume 10 (2017), pp. 2662-2670 | DOI

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