New iterative schemes for solving variational inequality and fixed points problems involving demicontractive and quasi-nonexpansive mappings in Banach spaces

[1]Ya. Alber, Metric and generalized Projection Operators in Banach space:properties and applications in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type,(A. G Kartsatos, Ed.), Marcel Dekker, New York (1996), pp. 15-50.AlberYa.Metric and generalized Projection Operators in Banach space:properties and applications in Theory and Applications of Nonlinear Operators of Accretive and Monotone TypeKartsatosA. G.Marcel DekkerNew York19961550Search in Google Scholar

[2]F. E. Browder, Convergenge theorem for sequence of nonlinear operator in Banach spaces, Z., 100 (1967) 201-225.BrowderF. E.Convergenge theorem for sequence of nonlinear operator in Banach spacesZ.1001967201225Search in Google Scholar

[3]P.L. Combettes, A block-iterative surrogate constraint splitting method for quadratic signal recovery, IEEE Transactions on Signal Processing 51(7), 1771-1782 (2003).CombettesP.L.A block-iterative surrogate constraint splitting method for quadratic signal recoveryIEEE Transactions on Signal Processing517177117822003Search in Google Scholar

[4]I. Cioranescu, Geometry of Banach space, duality mapping and nonlinear problems, Kluwer, Dordrecht, (1990).CioranescuI.Geometry of Banach space, duality mapping and nonlinear problemsKluwerDordrecht1990Search in Google Scholar

[5]C. E. Chidume, Geometric Properties of Banach spaces and Nonlinear Iterations, Springer Verlag Series: Lecture Notes in Mathematics, Vol. 1965, (2009), ISBN 978-1-84882-189-7.ChidumeC. E.Geometric Properties of Banach spaces and Nonlinear IterationsSpringer Verlag Series: Lecture Notes in Mathematics19652009ISBN 978-1-84882-189-7Search in Google Scholar

[6]C.E. Chidume, The solution by iteration of nonlinear equations in certain Banach spaces, J. Nigerian Math. Soc., 3 (1984), 57-62.ChidumeC.E.The solution by iteration of nonlinear equations in certain Banach spacesJ. Nigerian Math. Soc.319845762Search in Google Scholar

[7]K. Goebel and W.A. Kirk, Topics in metric fixed poit theory, Cambridge Studies, in Advanced Mathemathics, Vol. 28, University Cambridge Press, Cambridge 1990.GoebelK.KirkW.A.Topics in metric fixed poit theoryCambridge Studies, in Advanced Mathemathics28University Cambridge PressCambridge1990Search in Google Scholar

[8]E. Hairer, S.P. Norsett, G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd edn. Springer Series in Computational Mathematics. Springer, Berlin (1993).HairerE.NorsettS.P.WannerG.Solving Ordinary Differential Equations I: Nonstiff Problems2ndSpringer Series in Computational Mathematics. SpringerBerlin1993Search in Google Scholar

[9]T.C. Lim, H.K. Xu, Fixed point theorems for assymptoticaly nonexpansive mapping, Nonliear Anal 22(1994), no. 11, 1345-1355.LimT.C.XuH.K.Fixed point theorems for assymptoticaly nonexpansive mappingNonliear Anal2219941113451355Search in Google Scholar

[10]G. Marino and H. K. Xu, A general iterative method for nonexpansive mappings in Hibert spaces, J. Math. Anal. Appl. 318 (2006), 43-52.MarinoG.XuH. K.A general iterative method for nonexpansive mappings in Hibert spacesJ. Math. Anal. Appl.31820064352Search in Google Scholar

[11]G. Marino, S.Bruno, and K. Erdal, Strong convergence theorem for strict pseudo-contractions in Hilbert spaces, Journal of Inequalities and Applications (2016) 2016 134. 10.1186/s13660-016-1072-6.MarinoG.BrunoS.ErdalK.Strong convergence theorem for strict pseudo-contractions in Hilbert spacesJournal of Inequalities and Applications2016201613410.1186/s13660-016-1072-6Open DOISearch in Google Scholar

[12]G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Math. Appl., 329(2007), 336-346.MarinoG.XuH.K.Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spacesJ. Math. Math. Appl.3292007336346Search in Google Scholar

[13]P. E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Analysis, 16, 899-912 (2008).MaingeP. E.Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimizationSet-Valued Analysis168999122008Search in Google Scholar

[14]A. Moudafi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl. 241, 46-55 (2000).MoudafiA.Viscosity approximation methods for fixed point problemsJ. Math. Anal. Appl.24146552000Search in Google Scholar

[15]Z. Opial, Weak convergence of sequence of succecive approximation of nonexpansive mapping, Bull. Am. Math. Soc. 73 (1967), 591 597.OpialZ.Weak convergence of sequence of succecive approximation of nonexpansive mappingBull. Am. Math. Soc.731967591597Search in Google Scholar

[16]B. Panyanak, Ishikawa iteration processes for multi-valued mappings in Banach Spaces, Comput. Math. Appl. 54 (2007), 872-877.PanyanakB.Ishikawa iteration processes for multi-valued mappings in Banach SpacesComput. Math. Appl.542007872877Search in Google Scholar

[17]S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, Journal of Mathematical Analysis and Applications, vol. 67, no. 2, pp. 274276, 1979.ReichS.Weak convergence theorems for nonexpansive mappings in Banach spacesJournal of Mathematical Analysis and Applications6722742761979Search in Google Scholar

[18]T.M.M. Sow, A new general iterative algorithm for solving a variational inequality problem with a quasi-nonexpansive mapping in Banach spaces, Communications in Optimization Theory, Vol. 2019 (2019), Article ID 9, pp. 1-12.SowT.M.M.A new general iterative algorithm for solving a variational inequality problem with a quasi-nonexpansive mapping in Banach spacesCommunications in Optimization Theory20192019Article ID 9112Search in Google Scholar

[19]H.K. Xu, An iterative approach to quadratic optimization problem, J. Optim. Theory Appl. 116 (2003) 659-678.XuH.K.An iterative approach to quadratic optimization problemJ. Optim. Theory Appl.1162003659678Search in Google Scholar

[20]H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991), no. 12, 1127-1138.XuH. K.Inequalities in Banach spaces with applicationsNonlinear Anal.1619911211271138Search in Google Scholar

[21]H.K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. 66 (2002), no. 2, 240 - 256.XuH.K.Iterative algorithms for nonlinear operatorsJ. London Math. Soc.6620022240256Search in Google Scholar

[22]H.K. Xu, M.A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl. 2015, 41 (2015).XuH.K.AlghamdiM.A.ShahzadN.The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spacesFixed Point Theory Appl.2015412015Search in Google Scholar

[23]Y. Yao, H. Zhou, Y. C. Liou, Strong convergence of modified Krasnoselskii-Mann iterative algorithm for nonexpansive mappings, J. Math. Anal. Appl. Comput. 29 (2009) 383-389.YaoY.ZhouH.LiouY. C.Strong convergence of modified Krasnoselskii-Mann iterative algorithm for nonexpansive mappingsJ. Math. Anal. Appl. Comput.292009383389Search in Google Scholar