پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 635 |
| تعداد مقالات | 9,313 |
| تعداد مشاهده مقاله | 67,881,153 |
| تعداد دریافت فایل اصل مقاله | 17,084,729 |
Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 16، دوره 14، شماره 2، اردیبهشت 2023، صفحه 175-193 اصل مقاله (548.54 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27076.3489 | ||
| نویسندگان | ||
| Akindele Adebayo Mebawondu* 1، 2؛ Paranjothi Pillay1؛ Ojen K. Narain1؛ Akindele Akano Onifade3؛ Mathew O. Adewole3 | ||
| 1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa | ||
| 2DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) | ||
| 3Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria | ||
| تاریخ دریافت: 13 اردیبهشت 1401، تاریخ بازنگری: 26 مرداد 1401، تاریخ پذیرش: 02 شهریور 1401 | ||
| چکیده | ||
| In this paper, we propose an iterative method for finding the common element of the set of fixed points of Reich-Suzuki nonexpansive mappings and the set of solutions of the variational inequalities problems in the framework of Hilbert spaces. In addition, we establish convergence results for these proposed iterative methods under some mild conditions. Furthermore, we establish analytically and numerically that our newly proposed iterative method converges to a common element of the set of fixed points of a Reich-Suzuki nonexpansive mapping and the set of solutions of the variational inequalities problems faster compared to some well-known iterative methods in the literature. Finally, we apply our proposed iterative method to approximate the solution of a convex minimization problem. The results obtained in this paper improve, extend and unify some related results in the literature. | ||
| کلیدواژه‌ها | ||
| Variational inequality problem؛ inertial iterative scheme؛ fixed point problem؛ Reich-Suzuki nonexpansive mappings | ||
| مراجع | ||
|
[1] H.A. Abass, A.A. Mebawondu and O.T. Mewomo, Some results for a new three iteration scheme in Banach spaces, Bull. Univ. Transilvania Brasov, Ser. III: Math. Inf. Phys. 11 (2018), no. 2, 1–18.
[2] M. Abass and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mate. Vesnik, 66 (2014), no. 2, 223–234. [3] M. Abbas, Z. Kadelburg and D.R. Sahu, Fixed point theorems for Lipschitzian type mappings in CAT(0) spaces, Math. Comp. Model. 55 (2012), 1418–1427. [4] R.P. Agarwal, D. O’Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Convex Anal. 8 (2007), no. 1, 61–79. [5] V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasicontractive operators, Fixed Point Theory Appl. 2 (2004), 97–105. [6] F.E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA. 54 (1965), 1041–1044. [7] P. Cholamijak and S. Suantai, Iterative variational inequalities and fixed point problem of nonexpansive semigroups, J. Glob. Optim. 57 (2013), 1277–1297. [8] P. Chuadchawna, A. Farajzadeh and A. Kaewcharoen, Fixed-point approximation of generalized nonexpansive mappings via generalized M-iteration in hyperbolic spaces, Int. J. Math. Sci. 2020 (2020), 1–8. [9] M. Ert¨urk, F. G¨ursoy and N. S¸im¸sek, S-iterative algorithm for solving variational inequalities, Int. J. Comput. Math. 98 (2021), no. 3, 435–448. [10] M. Ert¨urk, F. G¨ursoy, Q. Ansari and V. Karakaya, Picard type iterative method with application to minimization problems and split feasibility problems, J.Nonlinear Convex Anal. 21 (2020), 943–951. [11] G. Ficher, Sul pproblem elastostatico di signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur, 34 (1963), 138–142. [12] G. Ficher, Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincci, Cl. Sci. Fis. Mat. Nat., Sez. 7 (1964), 91–140. [13] F. Giannessi, Vector variational inequalities and vector equilibria, Mathematical theories, 38, Kluwer Academic publisher, Dordrecht, 2000. [14] F. Gursoy, M. Ert¨urk and M. Abbas Picard-type iterative algorithm for general variational inequalities and nonexpansive mappings, Numer. Algor. 83 (2020), 867–883. [15] F. Gursoy, A Picard-S iterative method for approximating fixed point of weak-contraction mappings, Filomat 30 (2016), 2829–2845. [16] S. Ishikawa, Fixed points by new iteration method, Proc. Amer. Math. Soc. 149 (1974), 147–150. [17] M.A. Krasnosel’skii, Two remarks on the method of successive approximations, Usp. Mat. Nauk. 10 (1955), 123–127. [18] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510. [19] M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), 217–229.
[20] G. Stampacchia, Formes bilinearies coercivities sur les ensembles convexes, C. R. Acad. Sci. Paris 258 (1964), 4413–4416. [21] B.S. Thakur, D. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings, App. Math. Comp. 275 (2016), 147–155. [22] K. Ullah and M. Arshad, Numerical reckoning fixed points for Suzuki generalized nonexpansive mappings via new iteration process, Filomat 32 (2018), no. 1, 187–196. [23] K. Ullah and M. Arshad, Some results for a new three iteration scheme in Banach spaces, U.P.B. Sci. Bull. Ser. A 79 (2018), no. 4, 113–122. [24] N.C. Wong, D.R. Sahu and J.C. Yao, Solving variational inequalities involving nonexpansive type mapping, Nonlinear Anal. 69 (2008), 4732–4753. | ||
|
آمار تعداد مشاهده مقاله: 16,387 تعداد دریافت فایل اصل مقاله: 2,117 |
||