Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings

References

• Korpelevich GM. The extragradient method for finding saddle points and other problems. Ekonomikai Matematicheskie Metody. 1976;12:747–756.
   Google Scholar
• Zhao X, Ng KF, Li C, et al. Linear regularity and linear convergence of projection-based methods for solving convex feasibility problems. Appl Math Optim. 2018;78:613–641. doi: 10.1007/s00245-017-9417-1
   Web of Science ®Google Scholar
• Bin Dehaish BA. Weak and strong convergence of algorithms for the sum of two accretive operators with applications. J Nonlinear Convex Anal. 2015;16:1321–1336.
   Web of Science ®Google Scholar
• Qin X, Cho SY, Wang L. Strong convergence of an iterative algorithm involving nonlinear mappings of nonexpansive and accretive type. Optimization. 2018;67:1377–1388. doi: 10.1080/02331934.2018.1491973
   Web of Science ®Google Scholar
• Ceng LC, Petrusel A, Yao JC, et al. Hybrid viscosity extragradient method for systems of variational inequalities, fixed points of nonexpansive mappings, zero points of accretive operators in Banach spaces. Fixed Point Theory. 2018;19(2):487–502. doi: 10.24193/fpt-ro.2018.2.39
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335. doi: 10.1007/s10957-010-9757-3
   PubMed Web of Science ®Google Scholar
• Takahashi W, Wen CF, Yao JC. The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space. Fixed Point Theory. 2018;19:407–420. doi: 10.24193/fpt-ro.2018.1.32
   Web of Science ®Google Scholar
• Qin X, Yao JC. Projection splitting algorithms for nonself operators. J Nonlinear Convex Anal. 2017;18:925–935.
   Web of Science ®Google Scholar
• Ceng LC, Sahu DR, Yao JC. A unified extragradient method for systems of hierarchical variational inequalities in a Hilbert space. J Inequal Appl 2014;2014:460, 32 pp. doi: 10.1186/1029-242X-2014-460
   Web of Science ®Google Scholar
• Qin X, Cho SY, Wang L. Iterative algorithms with errors for zero points of m-accretive operators. Fixed Point Theory Appl. 2013;2013:148. doi: 10.1186/1687-1812-2013-148
   Google Scholar
• Ansari QH, Babu F, Yao JC. Regularization of proximal point algorithms in Hadamard manifolds. J Fixed Point Theory Appl. 2019;21:21–25. doi: 10.1007/s11784-019-0658-2
   Web of Science ®Google Scholar
• Cho SY. On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems. Appl Math Comput. 2014;235:430–438.
   Web of Science ®Google Scholar
• Shang M. A descent-like method for fixed points and split conclusion problems. J Appl Numer Optim. 2019;1:91–101.
   Google Scholar
• Qin X, Cho SY, Kang SM. On hybrid projection methods for asymptotically quasi-φ-nonexpansive mappings. Appl Math Comput. 2010;215:3874–3883.
   Web of Science ®Google Scholar
• Van Tuyen N, Yao JC, Wen CF. A note on approximate Karush-Kuhn-Tucker conditions in locally Lipschitz multiobjective optimization. Optim Lett. 2019;13:163–174. doi: 10.1007/s11590-018-1261-y
   Web of Science ®Google Scholar
• Cho SY, Qin X, Wang L. Strong convergence of a splitting algorithm for treating monotone operators. Fixed Point Theory Appl. 2014;2014:94. Article ID 94. doi: 10.1186/1687-1812-2014-94
   Google Scholar
• Nguyen LV, Qin X. Some results on strongly pseudomonotone quasi-variational inequalities. Set-Valued Var Anal. 2019. doi:10.1007/s11228-019-00508-1
   Web of Science ®Google Scholar
• Qin X, Cho SY, Kang SM. Strong convergence of shrinking projection methods for quasi-φ-nonexpansive mappings and equilibrium problems. J Comput Appl Math. 2010;234:750–760. doi: 10.1016/j.cam.2010.01.015
   Web of Science ®Google Scholar
• Liu L. Iterative methods for fixed points and zero points of nonlinear mappings with applications. Optimization. 2019. doi:10.1080/02331934.2019.1613404
   Web of Science ®Google Scholar
• Chang SS, Wen CF, Yao JC. Common zero point for a finite family of inclusion problems of accretive mappings in Banach spaces. Optimization. 2018;67:1183–1196. doi: 10.1080/02331934.2018.1470176
   Web of Science ®Google Scholar
• Ceng LC, Latif A, Ansari QH, et al. Hybrid extragradient method for hierarchical variational inequalities. Fixed Point Theory Appl. 2014, 2014:222, 35 pp. doi: 10.1186/1687-1812-2014-222
   Google Scholar
• Kraikaew R, Saejung S. Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces. J Optim Theory Appl. 2014;163:399–412. doi: 10.1007/s10957-013-0494-2
   Web of Science ®Google Scholar
• Ceng LC, Liou YC, Wen CF. Composite relaxed extragradient method for triple hierarchical variational inequalities with constraints of systems of variational inequalities. J Nonlinear Sci Appl. 2017;10:2018–2039. doi: 10.22436/jnsa.010.04.58
   Google Scholar
• Thong DV, Hieu DV. Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems. Numer Algorithms. 2019;80:1283–1307. doi: 10.1007/s11075-018-0527-x
   Web of Science ®Google Scholar
• Qin X, Cho SY. Convergence analysis of a monotone projection algorithm in reflexive Banach spaces. Acta Math Sci. 2017;37:488–502. doi: 10.1016/S0252-9602(17)30016-4
   Web of Science ®Google Scholar
• Cho SY et al. Viscosity approximation splitting methods for monotone and nonexpansive operators in Hilbert spaces. J Nonlinear Convex Anal. 2018;19:251–264.
   Web of Science ®Google Scholar
• Chang SS, Wen CF, Yao JC. Zero point problem of accretive operators in Banach spaces. Bull Malaysian Math Sci Soc. 2019;42:105–118. doi: 10.1007/s40840-017-0470-3
   Web of Science ®Google Scholar
• Cho SY, Bin Dehaish BA, Qin X. Weak convergence of a splitting algorithm in Hilbert spaces. J Appl Anal Comput. 2017;7:427–438.
   Google Scholar
• Thong DV, Van Hieu D. Modified subgradient extragradient method for variational inequality problems. Numer Algorithms. 2018;79:597–610. doi: 10.1007/s11075-017-0452-4
   Web of Science ®Google Scholar
• Qin X, Cho SY, Wang L. A regularization method for treating zero points of the sum of two monotone operators. Fixed Point Theory Appl. 2014;2014:75. doi: 10.1186/1687-1812-2014-75
   Google Scholar
• Qin X, Yao JC. Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators. J Inequal Appl. 2016;2016:232. doi: 10.1186/s13660-016-1163-4
   Web of Science ®Google Scholar
• Rezapour S, Zakeri SH. Strong convergence theorems for δ-inverse strongly accretive operators in Banach spaces. Appl Set-Valued Anal Optim. 2019;1:39–52.
   Google Scholar
• Cho SY, Kang SM. Approximation of common solutions of variational inequalities via strict pseudocontractions. Acta Math Sci. 2012;32:1607–1618. doi: 10.1016/S0252-9602(12)60127-1
   Web of Science ®Google Scholar
• Qin X, Petrusel A, Yao JC. CQ iterative algorithms for fixed points of nonexpansive mappings and split feasibility problems in Hilbert spaces. J Nonlinear Convex Anal. 2018;19:157–165.
   Web of Science ®Google Scholar
• Cai G, Shehu Y, Iyiola OS. Strong convergence results for variational inequalities and fixed point problems using modified viscosity implicit rules. Numer Algorithms. 2018;77:535–558. doi: 10.1007/s11075-017-0327-8
   Web of Science ®Google Scholar
• Goebel K, Reich S. Uniform convexity, hyperbolic geometry, and nonexpansive mappings. New York: Marcel Dekker; 1984.
   Google Scholar
• Xu HK, Kim TH. Convergence of hybrid steepest-descent methods for variational inequalities. J Optim Theory Appl. 2003;119:185–201. doi: 10.1023/B:JOTA.0000005048.79379.b6
   Web of Science ®Google Scholar
• Lim TC, Xu HK. Fixed point theorems for asymptotically nonexpansive mappings. Nonlinear Anal. 1994;22:1345–1355. doi: 10.1016/0362-546X(94)90116-3
   Web of Science ®Google Scholar