# Fixed and common fixed point results for cyclic mappings of $\Omega$-distance

Volume 9, Issue 3, pp 727--735 Publication Date: March 24, 2016
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### Authors

Wasfi Shatanawi - Department of Mathematics, Faculty of Science, Hashemite University, Zarqa, Jordan. Anwar Bataihah - Department of Mathematics, Faculty of Science, Irbid National University, Zarqa, Jordan. Ariana Pitea - Department of Mathematics and Informatics, University Politehnica of Bucharest, Bucharest, 060042, Romania.

### Abstract

Jleli and Samet in [M. Jleli, B. Samet, Int. J. Anal., 2012 (2012), 7 pages] pointed out that some of fixed point theorems in G-metric spaces can be derived from classical metric spaces. In this paper, we utilize the concept of $\Omega$-distance in sense of Saadati et al. [R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Math. Comput. Modeling, 52 (2010), 797-801] to introduce new fixed point and common fixed point results for mappings of cyclic form, through the concept of G-metric space in sense of Mustafa and Sims [ Z. Mustafa, B. Sims, J. Nonlinear Convex Anal., 7 (2006), 289-297]. We underline that the method of Jleli and Samet cannot be applied to our results.

### Keywords

• Nonlinear contraction
• G-metric space
• common fixed point
• $\Omega$-distance.

•  47H10
•  54H25

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