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Convergence theorems by monotone hybrid algorithms for a family of generalized nonexpansive mappings and maximal monotone operators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 29، دوره 14، شماره 6، شهریور 2023، صفحه 357-369 اصل مقاله (406.99 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29593.4201 | ||
| نویسندگان | ||
| Mathew O. Aibinu* 1، 2؛ Sibusiso Moyo3، 4 | ||
| 1Institute for Systems Science and KZN e-Skills CoLab, Durban University of Technology, South Africa | ||
| 2DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa | ||
| 3Department of Applied Mathematics and School for Data Science and Computational Thinking, Stellenbosch University, South Africa | ||
| 4National Institute for Theoretical and Computational Sciences (NITheCS), South Africa | ||
| تاریخ دریافت: 23 دی 1401، تاریخ بازنگری: 28 بهمن 1401، تاریخ پذیرش: 28 اسفند 1401 | ||
| چکیده | ||
| Finding a zero of a maximal monotone operator is known as one of the most impressive problems which are associated with convex analysis and mathematical optimization. Akin to this is solving the fixed point problems of the class of nonexpansive mappings, which constitutes an important part of nonlinear operators with fascinating applications in several areas such as signal processing and image restoration. This study presents a monotone hybrid algorithm for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a family of a generalized nonexpansive mapping in a Banach space. Suitable conditions under which the algorithm converges strongly are established. | ||
| کلیدواژه‌ها | ||
| Generalized؛ Maximal monotone؛ Nonexpansive؛ Retraction؛ Algorithm | ||
| مراجع | ||
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[1] F. Ali, J. Ali and JJ. Nieto, Some observations on generalized non-expansive mappings with an application, Comp. Appl. Math. 39 (2020), no. 2, 74. [2] S. Alizadeh and F. Moradlou, A monotone hybrid algorithm for a family of generalized nonexpansive mappings in Banach spaces, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 2347–2359. [3] V. Berinde and M. Pacurar, Kannan’s fixed point approximation for solving split feasibility and variational inequality problems, J. Comput. Appl. Math. 386 (2021), 113217. [4] C. Byrne, A unified treatment of some iterative algorithms in signal processing and image restoration, Inverse Probl. 20 (2004), 103–120. [5] C.E. Chidume, A. Adamu and M.O. Nnakwe, Strong convergence of an inertial algorithm for maximal monotone inclusions with applications, Fixed Point Theory Appl. 2020 (2020), 13. [6] W. Cholamjiak, S.A. Khan, D. Yambangwai and K.R. Kazmi, Strong convergence analysis of common variational inclusion problems involving an inertial parallel monotone hybrid method for a novel application to image restoration, RACSAM 114 (2020), 1–20. [7] V. Dadashi and M. Postolache, Forward-backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators, Arab. J. Math. 9 (2020), 89–99. [8] T. Ibaraki and W. Takahashi, Block iterative methods for finite family of generalized nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 29 (2008), 362–375. [9] T. Ibaraki and W. Takahashi, A new projection and convergence theorems for the projections in Banach spaces, J. Approx. Theory 149 (2007), 1–14. [10] S. Kamimura, F. Kohsaka and W. Takahashi, Weak and strong convergence theorems for maximal monotone operators in a Banach space, Set-Valued Anal. 12 (2004), 417–429. [11] S. Kamimura and W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim. 13 (2002), 938–945. [12] C. Klin-eam, S. Suantai and W. Takahashi, Strong convergence theorems by monotone hybrid method for a family generalized nonexpansive mappings in Banach spaces, Taiwanese J. Math. 16 (2012), no. 6, 1971–1989. [13] F. Kohsaka and W. Takahashi, Existence and approximation of fixed points of firmly nonexpansivetype mappings in Banach spaces, SIAM J. Optim. 19 (2008), no. 2, 824–835. [14] F. Kohsaka and W. Takahashi Generalized nonexpansive retractions and a proximal-type algorithm in Banach spaces, J. Nonlinear Convex Anal. 8 (2007), 197–209. [15] F. Kohsaka and W. Takahashi, Strong convergence of an iterative sequence for maximal monotone operators in a Banach space, Abstr. Appl. Anal. 2004 (2004), 239–249. [16] M.A. Noor, K.I. Noor and M.T. Rassias, New trends in general variational inequalities, Acta Appl. Math. 170 (2020), 981–1064. [17] B. Patir, N. Goswami, V.N. Mishra, Some results on fixed point theory for a class of generalized nonexpansive mappings, Fixed Point Theory Appl. 2018 (2018), 19. https://doi.org/10.1186/s13663-018-0644-1 [18] X. Qin and Y. Su, Strong convergence of monotone hybrid method for fixed point iteration processes, J. Syst. Sci. Complexity 21 (2008), 474–482. [19] S. Reich and A.J. Zaslavski, On a class of generalized nonexpansive mappings, Mathematics 8 (2020), no. 7, 1085. [20] R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14 (1976), no. 5, 877–898. [21] R.T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75–88. [22] Y. Shehu, Q.L. Dong and D. Jiang, Single projection method for pseudo-monotone variational inequality in Hilbert spaces, Optimization 68 (2019), no. 1, 385–409. [23] Y. Shehu, Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces, Results Math. 74 (2019), no. 4, 138. [24] D.V. Thong, N.T. Vinh and Y.J. Cho, A strong convergence theorem for Tseng’s extragradient method for solving variational inequality problems, Optim. Lett. 14 (2020), 1157–1175. [25] K. Ullah, J. Ahmad and M. Sen, On generalized nonexpansive maps in Banach spaces, Computation 8 (2020), no. 3, 61. [26] C. Zalinescu, On uniformly convex functions, J. Math. Anal. Appl. 95 (1983), 344–374. | ||
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