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Convexity in G-metric spaces and approximation of fixed points by Mann iterative process | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 162، دوره 13، شماره 1، خرداد 2022، صفحه 1957-1964 اصل مقاله (330.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21435.2259 | ||
| نویسندگان | ||
| Isa Yildirim* 1؛ Safeer Hussain Khan2 | ||
| 1Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey | ||
| 2Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar | ||
| تاریخ دریافت: 03 مهر 1399، تاریخ بازنگری: 18 تیر 1400، تاریخ پذیرش: 28 مرداد 1400 | ||
| چکیده | ||
| In this paper, we first define the concept of convexity in G-metric spaces. We then use Mann iterative process in this newly defined convex G-metric space to prove some convergence results for some classes of mappings. In this way, we can extend several existence results to those approximating fixed points. Our results are just new in the setting. | ||
| کلیدواژهها | ||
| Convex structure؛ Convex G-metric space؛ Mann iterative process؛ convergence | ||
| مراجع | ||
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[1] A.R. Khan and M.A. Ahmed, Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications, Comput. Math. Appl. 59 (2010) 2990– 2995. [2] J.K. Kim, K. S. Kim and S.M. Kim, Convergence theorems of implicit iteration process for for finite family of asymptotically quasi-nonexpansive mappings in convex metric space, Nonlinear Anal. Convex Anal. 1484 (2006) 40–51. [3] Q.Y. Liu, Z.B. Liu and N.J. Huang, Approximating the common fixed points of two sequences of uniformly quasiLipschitzian mappings in convex metric spaces, Appl. Math. Comp. 216 (2010) 883–889. [4] G. Modi and B. Bhatt, Fixed point results for weakly compatible mappings in convex G-metric space, Int. J. Math. Stat. Inven. 2(11) (2014) 34–38. [5] Z. Mustafa, A New Structure For Generalized Metric Spaces – With Applications To Fixed Point Theory, PhD Thesis, the University of Newcastle, Australia, 2005. [6] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear and Convex Anal. 7(2) (2006) 289–297. [7] Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl. 2008 (2008) Article ID 189870. [8] Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci. 2009 (2009) Article ID 283028. [9] Z. Mustafa and H. Obiedat, A fixed point theorem of Reich in G-metric spaces, CUBO Math. J. 12(1) (2010) 83–93. [10] W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970) 142–149. [11] I. Yildirim and S. H. Khan, Convergence theorems for common fixed points of asymptotically quasi-nonexpansive mappings in convex metric spaces, Appl. Math. Comput. 218(9) (2012) 4860–4866. | ||
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