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Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space | ||
| Journal of Hyperstructures | ||
| دوره 13، شماره 1، 2024، صفحه 94-108 اصل مقاله (297.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2024.14426.1005 | ||
| نویسندگان | ||
| Omprash Sahu* 1؛ Amitabh Banerjee2 | ||
| 1Department of Mathematics, Babu Pandhri Rao Kridatt Govt.College Silouti, Dhamtari, Raipur(C.G.), India | ||
| 2Principal, Govt. J.Y. Chhattisgarh College, Raipur, India | ||
| چکیده | ||
| In this paper, we establish strong and weak convergence theorems for Suzuki's generalized nonexpansive mapping in uniformly convex Banach spaces using the iterative scheme introduced by Panigrahy et al [9]. Next, we see an example of Suzuki's generalized nonexpansive mapping, which is not a nonexpansive mapping. Using this example and some numerical tests, we infer empirically that the Panigrahy iteration process converges faster than the Krasnoselskij, Thakur, and M-iteration processes. | ||
| کلیدواژهها | ||
| Fixed Point؛ Uniformly convex Banach space؛ Suzuki generalized nonexpansive mapping؛ Panigrahy iteration؛ Convergence Theorem | ||
| مراجع | ||
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[1] A. A. Mebawondu, and O.T. Mewomo, Fixed point results for a new three steps iteration process, Annals of the University of Craiova, Mathematics and Computer Science Series, 46, no.2, (2019), 298-319. [2] A. Aghanians, K. Fallahi, and K. Nourouzi, Fixed points for G-contractions on uniform spaces endowed with a graph, Fixed Point Theory Appl., (2012), 2012, 182. [3] B. S. Thakur, D. Thakur, and M. Postolache, A new iterative scheme for numerical reckoning xed points of Suzukis generalized nonexpansive mappings, App. Math. Comp., 275 (2016), 147-155. [4] F. Gursoy, and V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, (2014) arXiv:1403.2546v2. [5] H. F. Senter, and W. G. Dotson, Approximating xed points of nonexpansive mappings, Proc. Am. Math. Soc., 44, no.2, (1974), 375-380. [6] J. Schu, Weak and strong convergence to xed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc., 43, no.1, (1991),153-159. [7] J. B. Diaz, and F.T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bull. Am. Math. Soc., 73, (1967), 516-519. [8] K. Goebel, and W. A. Kirk, Topic in metric xed point theory, Cambridge University Press, (1990). [9] K. Panigrahy, and D. Mishra, A note on a faster- xed point iterative method, The Journal of Analysis, (2022), DOI: https://doi.org/10.1007/s41478-022-00485-z. [10] K. Ullah, and M. Arshad, Numerical reckoning xed point for Suzuki generalized nonexpansive mappings via new iteration process, Filomat, 32, no.1, (2018), 187-196. [11] M.A.Krasnoselskij, Two remarks on the method of successive approximations (Russian) , Uspehi Mat. Nauk., 10, no.1, (1955), 123-127. [12] O. Sahu, and A. Banerjee, Convergence Results for Mean Nonexpansive Mappings in Uniformly Convex Banach Space, Creat. Math. Inform., 32, no.2, (2023), 219-227. [13] S. Hassan, M. De la Sen, P.Agarwal, Q. Ali, and A. Hussain, A New Faster Iterative Scheme for Numerical Fixed Points Estimation of Suzukis Generalized Nonexpansive Mappings, Math. Probl. Eng., (2020), Article ID 3863819, 9 pp. [14] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44, (1974), 147-150. [15] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl., 340, (2008), 1088-1095. [16] W.R.Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4,(1953), 506-510. [17] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math. Soc., 73, no.4, (1967), 591-598. | ||
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