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Convergence analysis and approximation of fixed point of multivalued generalized $\alpha$-nonexpansive mapping in uniformly convex Banach space | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 5، دوره 14، شماره 2، اردیبهشت 2023، صفحه 45-74 اصل مقاله (680.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27791.3715 | ||
| نویسندگان | ||
| Unwana Udofia* ؛ Donatus Ikechi Igbokwe | ||
| Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria | ||
| تاریخ دریافت: 22 تیر 1401، تاریخ بازنگری: 27 مرداد 1401، تاریخ پذیرش: 02 شهریور 1401 | ||
| چکیده | ||
| Recently, the authors introduce a four-step iterative algorithm called the UD-iteration scheme (Udofia and Igbokwe [35]). Here we introduce the multivalued version of the UD-iteration scheme and show that it can be used to approximate the fixed points of multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings. we prove strong and weak convergence of the iteration scheme to the fixed point of multivalued generalized $\alpha$-nonexpansive mapping. We also prove that the scheme is $\varUpsilon$-stable and Data dependent. Convergence analysis shows that the multivalued UD-iteration scheme has a faster rate of convergence for multivalued contraction and multivalued generalized $\alpha$-nonexpansive mappings than some well-known existing iteration schemes in the literature. | ||
| کلیدواژه‌ها | ||
| Uniformly convex Banach space؛ Multivalued generalized $\alpha$-nonexpansive Mapping؛ Convergence؛ Data dependence؛ Stability | ||
| مراجع | ||
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[1] M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik. 66 (2014), no. 2, 223–234.
[2] A. Abkar and M. Eslamian, A fixed point theorem for generalized nonexpansive multivalued mappings, Fixed Point Theory 12 (2011), no. 2, 241–246. [3] R.P. Agarwal, D. Oregan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8 (2007), no. 1, 61–79. [4] D. Ariza-Ruiz, C. Hermandez Linares, E. Llorens-Fuster and E. Moreno-Galvez, On α-nonexpansive mappings in Banach spaces, Carpath. J. Math. 32 (2016), 13–28. [5] K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74 (2011), 4387–4391. [6] K. Aoyama, S. Iemoto, F. Kohsaka and W. Takahashi, Fixed point and ergodic theorems for λ-hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 11 (2010), 335–343. [7] M. Bachar and M.A. Khamsi, On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces, Fixed Point Theory Appl. 2015 (2015), 160. [8] V. Berinde, Generalized contractions and applications (Romanian), Editura Cub Press 22, Baia Mare 1997. [9] V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasicontractive operators, Fixed Point Theory Appl. 2 (2004), 97–105. [10] B.A.B. Dehaish and M.A. Khamsi, Mann iteration process for monotone nonexpansive mappings, Fixed Point Theory Appl. 2015 (2015), 177. [11] J. Garc´ea-Falset, E. Llorens-Fuster and E. Moreno-G`a ´alvez, Fixed point theory for multivalued generalized nonexpansive mappings, Appl. Anal. Discrete Math. 6 (2012), 265–286. [12] K. Goebel and W.A. Kirk, Topics in Metric Fixed Point Theory, in: Cambridge Studies in Advanced Mathematics, vol. 28, Cambridge University Press, Cambridge, 1990. [13] K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 83, Marcel Dekker Inc., New York, 1984. [14] M.A. Harder, Fixed point theory and stability results for fixed point iteration procedures, PhD thesis, University of Missouri-Rolla, Missouri, 1988. [15] T.L. Hicks and J.R. Kubicek, On the Mann iteration process in Hilbert space, J. Math. Anal. Appl. 59 (1977), 498–504. [16] N. Hussain, K. Ullah and M. Arshad, Fixed point approximation for Suzuki generalized nonexpansive mappings via new iteration process, J. Nonlinear and Convex Anal. 19 (2018), no. 8, 1383–1393. [17] H. Iqbal, M. Abbas and S.M. Husnine, Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces, Numer. Algor. 85 (2020), no. 3, 1029–1049. [18] S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc. 4 (1974), no. 1, 147–150. [19] W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Month. 72 (1965), 1004–1006. [20] S. Maldar, F. G¨ursoy, Y. Atalan and M. Abbas, On a three-step iteration process for multivalued Reich-Suzuki type α-nonexpansive and contractive mappings, J. Appl. Math. Comput. 68 (2022), no. 2, 863–883.
[21] W.R. Mann, Mean value methods in iteration, Proc. Am. Math. Soc. 4 (1953), 506–510. [22] E. Naraghirad, N.C. Wong and J.C. Yao, Approximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces, Fixed Point Theory Appl. 2013 (2013), 57. [23] M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), 217–229. [24] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591–597.
[25] R. Pant and R. Shukla, Approximating fixed points of generalized α-nonexpansive mapping in Banach spaces, Numer. Funct. Anal. Optim. 38 (2017) 248–266. [26] H. Piri, B. Daraby, S. Rahrovi and M. Ghasemi, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process, Numer. Algor. 81 (2019), 1129—1148. [27] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Aust. Math. Soc. 43 (1991), no. 1, 153–159. [28] N. Shahzad and H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71 (2009), no. 3-4, 838–844. [29] R. Shukla, R. Pant and M. De la Sen, Generalized α-nonexpansive mappings in Banach spaces, Fixed Point Theory and Appl. 2017 (2016), no. 1, 1–4. [30] S.M. Soltuz and T. Grosan, Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl. 2008 (2008), 1–7. [31] Y.S. Song, K. Promluang, P. Kumam and Y.J. Cho, Some convergence theorems of the Mann iteration for monotone α-nonexpansive mappings, Appl. Math. Comput. 287-288 (2016), 74–82. [32] T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008), no. 2, 1088–1095. [33] B.S. Thakur, D. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings, Appl. Math. Comput. 275 (2016), 147–155. [34] U.E. Udofia and D.I. Igbokwe, Convergence theorems for monotone generalized α-nonexpansive mappings in ordered banach space by a new four-step iteration process with application, Commun. Nonlinear Anal. 9 (2020), no. 2, 1 17. [35] U.E. Udofia and D.I. Igbokwe, A novel iterative algorithm with application to fractional differential equation, preprint. [36] K. Ullah, J. Ahmad and M, de la Sen, On generalized nonexpansive maps in Banach spaces, Comput. 8 (2020), no. 3, 61. [37] K. Ullah and M. Arshad, New iteration process and numerical reckoning fixed points in Banach spaces, U.P.B.S. Bull. Series A 79 (2017), 113–122. [38] K. Ullah and M. Arshad, Numerical reckoning fixed points for Suzuki generalized nonexpansive mappings via new iteration process, Filomat, 32 (2018), 187–196. [39] X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. 113 (1991), 727–731. [40] H.K. Xu, Inequality in Banach spaces with applications, Nonlinear Anal. 16 (1991), 1127–1138. [41] H. Xu, Iterative methods for the split feasibility problem in infnite-dimensional Hilbert spaces, Inverse Probl. 26 (2010), 17. | ||
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