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Two step size algorithms for strong convergence for a monotone operator in Banach spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 14، شماره 10، دی 2023، صفحه 217-225 اصل مقاله (384.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.27501.3626 | ||
| نویسندگان | ||
| John T. Mendy* ؛ Furmose Mendy | ||
| Mathematics Department, University of The Gambia, Brikama Campus, Gambia | ||
| تاریخ دریافت: 28 خرداد 1401، تاریخ پذیرش: 07 فروردین 1402 | ||
| چکیده | ||
| For $p\geq 2$, let $E$ be a $2$ uniformly smooth and $p$ uniformly convex real Banach spaces and let a mapping $\displaystyle \Phi : E \to E^{*}$ be Lipschitz, and strongly monotone such that $\displaystyle \Phi^{-1}(0)\neq \emptyset$. For an arbitrary $(\{\xi_{1}\}, \{\psi_{1}\})\in E$, we define the sequences $\{\xi_{n}\}$ and $\{\psi_{n}\}$ by \begin{equation*} \left\{ \begin{array}{ll} \psi_{n+1} = J^{-1}(J\xi_{n} - \theta_{n}\Phi\xi_{n}), & \hbox{$n\geq 0$} \\ \xi_{n+1} = J^{-1}(J\psi_{n+1} - \lambda_{n}\Phi\psi_{n+1}), & \hbox{$n\geq 0$} \\ \end{array} \right. \end{equation*} where $\lambda_{n}$ and $\theta_{n}$ are positive real number and $J$ is the duality mapping of $E$. Letting $(\lambda_{n}, \theta_{n})\in (0,\Lambda_{p})$ where $\Lambda_{p} >0$, then $\xi_{n}$ and $\psi_{n}$ converges strongly to $\xi^{*}$, a unique solution of the equation $\Phi \xi = 0$. | ||
| کلیدواژه‌ها | ||
| Lipschitz؛ Equations؛ generalized monotone؛ Bounded | ||
| مراجع | ||
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[1] Y. Alber, Metric and generalized projection operator in Banach space: Properties and applications, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type (ed. A. G. Kartsatos), Marcel Dekker, New York, 1996, pp. 15-50. [2] Y. Alber and S. Guerre-Delabiere, On the projection methods for fixed point problems, Analysis (Munich) 21 (2001), no. 1, 17–39. [3] Y. Alber and T. Ryazantseva, Nonlinear Ill Posed Problems of Monotone Type, Springer, London, UK, 2006. [4] Y.B. El Yekheir, J.T. Mendy, T.M.M. Sow, and N. Djitte, Proximal point algorithms for fixed point problem and convex minimization problem, Int. J. Math. Anal. 14 (2020), no. 1, 27–44. [5] F.E. Browder, Nonlinear mappings of nonexpansive and accretive-type in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), no. 6, 875–882. [6] C.E. Chidume, Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings, Proc. Amer. Math. Soc. 99 (1987), no. 2, 283–288. [7] C.E. Chidume, A. Adamu, and L.C. Okereke, A Krasnoselskii-type algorithm for approximating solutions of variational inequality problems and convex feasibility problems, J. Nonlinear Var. Anal. 2 (2018), 203–218. [8] C.E. Chidume, A.U. Bello, and B. Usman, Krasnoselskii-type algorithm for zeros of strongly monotone Lipschitz maps in classical Banach spaces, SpringerPlus 4 (2015), 297. [9] C.E. Chidume and M.O. Osilike, Iterative solution of nonlinear integral equations of Hammerstein-type, J. Niger. Math. Soc. Appl. Anal. 11 (1992), 9–18. [10] C.E. Chidume and M.O. Osilike, Iterative solutions of nonlinear accretive operator equations in arbitrary Banach spaces, Nonlinear Anal. Theory Methods Appl. 36 (1999), no. 7, 863–872. [11] S.Y. Cho, X. Qin, and L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl. 2014 (2014), 94. [12] I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Mathematics and Its Applications, 62, Springer, Dordrecht, 1990. [13] N. Djitte, J.T. Mendy, and T.M.M. Sow, Computation of zeros of monotone type mappings: on Chidume’s open problem, J. Aust. Math. Soc. 108 (2020), no. 2, 278–288. [14] S. Kamimura and W. Takahashi, Strong convergence of proximal-type algorithm in Banach space, SIAM J. Optim. 13 (2002), no. 3, 938–945. [15] S. Khorasani and A. Adibi, Analytical solution of linear ordinary differential equations by differential transfer, Elect. J. Diff. Equ. 79 (2003), 1–18. [16] N. Lehdili and A. Moudafi, Combining the proximal algorithm and Tikhonov regularization, Optim. 37 (1996), no. 3, 239–252. [17] B. Martinet, Regularisation d inequations variationnelles par approximations successives, Rech. Oper. 4 (1970), 154–158. [18] J.T. Mendy, M. Sene, and N. Djitte, Algorithm for zeros of maximal monotone mappings in classical Banach spaces, Int. J. Math. Anal. 11 (2017), no. 11, 551–570. [19] J. Mendy and R. Shukla, Viscosity like implicit methods for zeros of monotone operators in Banach spaces, Khayyam J. Math. 8 (2022), no. 1, 53–72. [20] A. Moudifi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl. 241 (2000), 46–55. [21] T. Mustafa, Approximate analytical solution of the nonlinear system of differential equations having asymptotically stable equilibrium, Filomat. 31 (2017), no. 9, 2633–2641. [22] S. Reich, A weak convergence theorem for alternating methods with Bergman distance, A.G. Kartsatos, (ed.) Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Lecture Notes in Pure and Applied Mathematics, Vol. 178. New York: Dekker, 1996, pp. 313–318. [23] S. Reich, Constructive techniques for accretive and monotone operators, Proc. Int. Conf. Appl. Nonlinear Anal., Univer. Texas at Arlington, Arlington, Texas, April 20-22, 1978, Appl. Nonlinear Anal., 1979, pp. 335–345. [24] S. Reich and S. Sabach, Two strong convergence theorems for a proximal method in reflexive Banach spaces, J. Numer. Funct. Anal. Optim. 31 (2010), no. 1, 22–44. [25] R.T. Rockafellar, Monotone operators and the proximal point algorithm, Trans. Amer. Math. Soc. 194 (1970), 75–88. [26] Y. Song and R. Chen, Strong convergence theorems on an iterative method for a family of finite non-expansive mappings, Appl. Math. Comput. 180 (2006), 275–287. [27] B.D. Stephen and H. Gareth, An inductive approximation to the solution of systems of nonlinear ordinary differential equations in pharmacokinetics-pharmacodynamics, J. Comp. Sci. Netw. 1 (2014), no. 4, 1000119. [28] W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000. [29] W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and Its Applications, Yokohama Publishers Inc, Yokohama, 2000. [30] W. Takahashi and Y. Ueda, On Reich’s strong convergence theorems for resolvents of accretive operators, J. Math. Anal. Appl. 104 (1984), no. 2, 546–553. [31] Y. Tang, Strong convergence of new algorithm for monotone operator in Banach spaces, Numer. Funct. Anal. Optim. 40 (2019), no. 12, 1426–1447. [32] H. Zegeye and N. Shahzad, An algorithm for a common minimum-norm zero of a finite family of monotone mappings in Banach spaces, J. Ineq. Appl. 2013 (2013), 556. | ||
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