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Further generalization of cyclic contraction for the best proximity point problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 28، دوره 14، شماره 9، آذر 2023، صفحه 379-284 اصل مقاله (354.49 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28176.3827 | ||
| نویسنده | ||
| Mohammad Reza Haddadi* | ||
| Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran | ||
| تاریخ دریافت: 02 شهریور 1401، تاریخ بازنگری: 16 آذر 1401، تاریخ پذیرش: 23 دی 1401 | ||
| چکیده | ||
| In this paper, we introduce a further generalization of the cyclic contraction mappings. Our main results generalize the recent related results proved by M. Jleli and B. Samet [8] and solve a best proximity point problem. In order to show the applicability of our main results, an example is presented. | ||
| کلیدواژهها | ||
| Best proximity point؛ Fixed point؛ Uniformly convex Banach space؛ Iterative sequence | ||
| مراجع | ||
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[1] J. Anuradha and P. Veeramani, Proximal pointwise contraction, Topology Appl. 156 (2009), no. 18, 2942–2948. [2] J. Caballero, J. Harjani and K. Sadarangani, A best proximity point theorem for Geraghty-contractions, Fixed Point Theory Appl. 2012 (2012), 1-9. [3] A.A. Eldred, W. A. Kirk, and P. Veeramani, Proximinal normal structure and relatively nonexpansive mappings, Studia Math. 171 (2005), no. 3, 283–293. [4] A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006), 1001–1006. [5] M.R. Haddadi and S.M. Moshtaghioun, Some Results on the Best Proximity Pair, Abstr. Appl. Anal. 2011 (2011), ID 158430, 9 pages. [6] M.R. Haddadi, V. Parvaneh and M. Moursalian, Global optimal approximate solutions of best proximity points, Filomat 35 (2021), no. 5, 159–167. [7] N. Hussain, V. Parvaneh, B. Samet and C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2015 (2015), 185. [8] M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014 (2014), 38. [9] H. Kumar Nashine, P. Kumam and C. Vetro, Best proximity point theorems for rational proximal contractions, Fixed Point Theory Appl. 2013 (2013), 95. [10] S. Sadiq Basha, Best proximity points: global optimal approximate solution, J. Global Optim. 49 (2011), no. 1, 15. [11] S. Sadiq Basha, Extensions of Banach’s contraction principle, Numer. Funct. Anal. Optim. 31 (2010), 569–576. [12] R.V. Sankar and P. Veeramani, Best proximity pair theorems for relatively nonexpansive mappings, Appl. Gen. Topol. 10 (2009), no. 1, 21–28. | ||
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