具图的Banach空间中G-渐近非扩张映像的不动点定理
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摘要
在Banach空间,文章引进了G-渐近非扩张映像的Mann迭代,并证明了这种迭代的弱收敛和强收敛性,文章的结果改进和推广了前人的结果。
In Banach space, we introduce the Mann iteration of G-asymptotically nonexpansive mappings, and prove the weak convergence and strong convergence of this iteration.The results of this paper improve and extend the results of previous studies.
In Banach space, we introduce the Mann iteration of G-asymptotically nonexpansive mappings, and prove the weak convergence and strong convergence of this iteration.The results of this paper improve and extend the results of previous studies.
引文
[1]F.E.Browder and W.V.Petryshyn,Construction of fixed points of nonlinear mappings in Hilbert space[J].J.Math.Anal.20.197-228(1967).
[2]C.Byrne,A unified treatment of some iterative algorithms in signal processing and image reconstruction[J].Inverse Problems,20.103-120(2004).
[3]C.I.Podilchuk and R.J.Mammone,Image recovery by convex projections using a least-squares constraint[J].Journal of the Optical Society of America,7.517-521(1990).
[4]Jachymski,J:The contraction principle for mappings on a metric space with a graph[J].Proc.Am.Math.Soc.136,1359-1373(2008).
[5]Alfuraidan,MR:Remarks on monotone multivalued mappings on a metric space with a graph[J].J.Inequal.Appl.(2015).doi:10.1186/s13660-015-0712-6.
[6]Alfuraidan,MR:Fixed points of monotone nonexpansive mappings with a graph.Fixed Point Theory Appl.[EB/OL].(2015).doi:10.1186/s13663-015-0299-0.
[7]Aleomraninejad,SMA,Rezapour,S,Shahzad,N:Some fixed point result on a metric space with a graph[EB/OL].(Topol.Appl.159,659-663(2012).
[8]Alfuraidan,MR,Khamsi,MA:Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with agraph.Fixed Point Theory[EB/OL].(Appl.(2015)doi:10.1186/s13663-015-0294-5.
[9]Tiammee,J,Kaekhao,A,Suantai,S:On Browder’s convergence theorem and Halpern iteration process for G-nonexpansive mappings in Hilbert spaces endowed with graph.Fixed Point Theory[EB/OL].(Appl.(2015).doi:10.1186/s13663-015-0436-9.
[10]Shahzad,N,Al-Dubiban,R:Approximating common fixed points of nonexpansive mappings in Banach spaces[J].Georgian Math.J.13(3),529-537(2006).
[11]Opial,Z,Weak convergence of successive approximations for nonexpansive mappings[J].Bull.Amer.Math.Soc.73.591-597(1967).
[12]H.F.Senter and W.G.Dotson Jr.,Approximating fixed points of nonexpansive mappings[J].Proceedings of the American Mathematical Society,44.375-380(1974).
[13]Tan,KK,Xu,HK Approximating fixed points of nonexpansive mappings by the Ishikawa iterations process[J].J.Math.Anal.Appl.178.301-308(1993).
[14]Xu,HK:Inequalities in Banach spaces with applications[J].Nonlinear Anal.16(12),1127-1138(1991).
[15]Suantai,S:Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings[J].J.Math.Anal.Appl.331,506-517(2005).
[2]C.Byrne,A unified treatment of some iterative algorithms in signal processing and image reconstruction[J].Inverse Problems,20.103-120(2004).
[3]C.I.Podilchuk and R.J.Mammone,Image recovery by convex projections using a least-squares constraint[J].Journal of the Optical Society of America,7.517-521(1990).
[4]Jachymski,J:The contraction principle for mappings on a metric space with a graph[J].Proc.Am.Math.Soc.136,1359-1373(2008).
[5]Alfuraidan,MR:Remarks on monotone multivalued mappings on a metric space with a graph[J].J.Inequal.Appl.(2015).doi:10.1186/s13660-015-0712-6.
[6]Alfuraidan,MR:Fixed points of monotone nonexpansive mappings with a graph.Fixed Point Theory Appl.[EB/OL].(2015).doi:10.1186/s13663-015-0299-0.
[7]Aleomraninejad,SMA,Rezapour,S,Shahzad,N:Some fixed point result on a metric space with a graph[EB/OL].(Topol.Appl.159,659-663(2012).
[8]Alfuraidan,MR,Khamsi,MA:Fixed points of monotone nonexpansive mappings on a hyperbolic metric space with agraph.Fixed Point Theory[EB/OL].(Appl.(2015)doi:10.1186/s13663-015-0294-5.
[9]Tiammee,J,Kaekhao,A,Suantai,S:On Browder’s convergence theorem and Halpern iteration process for G-nonexpansive mappings in Hilbert spaces endowed with graph.Fixed Point Theory[EB/OL].(Appl.(2015).doi:10.1186/s13663-015-0436-9.
[10]Shahzad,N,Al-Dubiban,R:Approximating common fixed points of nonexpansive mappings in Banach spaces[J].Georgian Math.J.13(3),529-537(2006).
[11]Opial,Z,Weak convergence of successive approximations for nonexpansive mappings[J].Bull.Amer.Math.Soc.73.591-597(1967).
[12]H.F.Senter and W.G.Dotson Jr.,Approximating fixed points of nonexpansive mappings[J].Proceedings of the American Mathematical Society,44.375-380(1974).
[13]Tan,KK,Xu,HK Approximating fixed points of nonexpansive mappings by the Ishikawa iterations process[J].J.Math.Anal.Appl.178.301-308(1993).
[14]Xu,HK:Inequalities in Banach spaces with applications[J].Nonlinear Anal.16(12),1127-1138(1991).
[15]Suantai,S:Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings[J].J.Math.Anal.Appl.331,506-517(2005).