非扩张半群公共不动点与广义变分不等式解的迭代收敛性
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摘要
引入一种新的非扩张半群显式粘滞迭代算法,使用这种显式粘滞迭代算法,在较弱条件下,在Hilbert空间中建立了非扩张半群公共不动点集与具有α-可逆g-强单调映象的广义变分不等式解集的公共元素的强收敛定理,推广和改进了相关结果.
We introduce a new kind of explicit viscosity iterative algorithms for nonexpansive semigroups,and by using this kind of explicit viscosity iterative algorithms,the strong convergence theorems to find a common element of the set of common fixed points for nonexpansive semigroups and the set of solutions of generalized variational inequalities with α-inverse g-strongly monotone mapping in Hilbert spaces are established under the weaker condition.This paper extends and improves the corresponding results.
We introduce a new kind of explicit viscosity iterative algorithms for nonexpansive semigroups,and by using this kind of explicit viscosity iterative algorithms,the strong convergence theorems to find a common element of the set of common fixed points for nonexpansive semigroups and the set of solutions of generalized variational inequalities with α-inverse g-strongly monotone mapping in Hilbert spaces are established under the weaker condition.This paper extends and improves the corresponding results.
引文
[1]Noor M A.General variational inequalities[J].Applied Mathematics Letters,1988(1):119-121.
[2]Stampacchia G.Formes bilineaires coercivites surles ensembles convexes[J].Comptes Rendusde Academiedes Sciences,1964,258:4413-4416.
[3]徐永春,何欣枫,侯志彬,等.Banach空间中Noor型变分不等式的广义投影法[J].数学物理学报,2010,30A(3):808-817.
[4]Takahashi W,Toyoda M.Weak convergence theorems for nonexpansive mappings and monotone mappings[J].J Optim Theory Appl,2003,118:417-428.
[5]Chen J M,Zhang L J,Fan T G.Viscosity approximation methods for nonexpansive mappings and monotone mappings[J].J Math Anal Appl,2007,334:1450-1461.
[6]张丽娟,陈俊敏,侯志彬.非扩张映射和广义变分不等式的粘滞逼近法[J].数学学报,2010,53(4):691-698.
[7]高雷阜,刘杰,高鼎.非扩张映射和广义变分不等式迭代算法[J].辽宁工程技术大学学报(自然科学版),2014,33(5):704-707.
[8]张树义,林媛,丛培根.非扩张映象和广义变分不等式的迭代收敛性[J].北华大学学报(自然科学版),2017,18(6):701-709.
[9]Plubtieng S,Punpaeng R.Fixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces[J].Math Comput Modell,2008,48(1-2):279-286.
[10]Zhang D,Qin X,Gu F.Approximation of common fixed points of nonexpansive semigroups in Hilbert spaces[J].Journal of Applied Mathematics Volume 2012,Article ID 417234,13 pages doi:10.1155/2012/417234.
[11]刘冬红,张树义,丛培根.渐近伪压缩型半群不动点的隐式迭代逼近[J].西华大学学报(自然科学版),2017,36(6):105-109.
[12]张树义,李丹,丛培根.增生算子零点的迭代逼近[J].北华大学学报(自然科学版),2017,18(2):1-7.
[13]赵美娜,张树义,郑晓迪.一类算子方程迭代序列的稳定性[J].轻工学报,2016,31(6):100-108.
[14]张树义,李丹,林媛,等.非自渐近非扩张型映象具误差的Reich-Takahashi粘滞迭代逼近[J].北华大学学报(自然科学版).2017,18(3):287-293.
[15]张树义,赵美娜,丛培根.广义渐近S-半压缩型映象迭代逼近[J].西华师范大学学报(自然科学版),2017,38(4):399-400.
[16]丛培根,张芯语,张树义.两有限族映象迭代序列的稳定性[J].鲁东大学学报(自然科学版),2017,33(4):296-301.
[17]林媛,张树义,丛培根.渐近非扩张型映象具有误差的迭代收敛性[J].石河子大学学报(自然科学版),2017,35(4):517-513.
[18]Wang S.A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces[J].Applied Math Lett,2011,24:901-907.
[19]Shimizu T,Takahashi W.Strong convergence to common fixed points of families of nonexpansive mappings[J].J Math Anal Appl,1997,211(1):71-83.
[20]Suzuki T.Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals[J].J Math Anal Appl,2005,305(1):227-239.
[21]Liu L S.Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194(1):114-125.
[2]Stampacchia G.Formes bilineaires coercivites surles ensembles convexes[J].Comptes Rendusde Academiedes Sciences,1964,258:4413-4416.
[3]徐永春,何欣枫,侯志彬,等.Banach空间中Noor型变分不等式的广义投影法[J].数学物理学报,2010,30A(3):808-817.
[4]Takahashi W,Toyoda M.Weak convergence theorems for nonexpansive mappings and monotone mappings[J].J Optim Theory Appl,2003,118:417-428.
[5]Chen J M,Zhang L J,Fan T G.Viscosity approximation methods for nonexpansive mappings and monotone mappings[J].J Math Anal Appl,2007,334:1450-1461.
[6]张丽娟,陈俊敏,侯志彬.非扩张映射和广义变分不等式的粘滞逼近法[J].数学学报,2010,53(4):691-698.
[7]高雷阜,刘杰,高鼎.非扩张映射和广义变分不等式迭代算法[J].辽宁工程技术大学学报(自然科学版),2014,33(5):704-707.
[8]张树义,林媛,丛培根.非扩张映象和广义变分不等式的迭代收敛性[J].北华大学学报(自然科学版),2017,18(6):701-709.
[9]Plubtieng S,Punpaeng R.Fixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces[J].Math Comput Modell,2008,48(1-2):279-286.
[10]Zhang D,Qin X,Gu F.Approximation of common fixed points of nonexpansive semigroups in Hilbert spaces[J].Journal of Applied Mathematics Volume 2012,Article ID 417234,13 pages doi:10.1155/2012/417234.
[11]刘冬红,张树义,丛培根.渐近伪压缩型半群不动点的隐式迭代逼近[J].西华大学学报(自然科学版),2017,36(6):105-109.
[12]张树义,李丹,丛培根.增生算子零点的迭代逼近[J].北华大学学报(自然科学版),2017,18(2):1-7.
[13]赵美娜,张树义,郑晓迪.一类算子方程迭代序列的稳定性[J].轻工学报,2016,31(6):100-108.
[14]张树义,李丹,林媛,等.非自渐近非扩张型映象具误差的Reich-Takahashi粘滞迭代逼近[J].北华大学学报(自然科学版).2017,18(3):287-293.
[15]张树义,赵美娜,丛培根.广义渐近S-半压缩型映象迭代逼近[J].西华师范大学学报(自然科学版),2017,38(4):399-400.
[16]丛培根,张芯语,张树义.两有限族映象迭代序列的稳定性[J].鲁东大学学报(自然科学版),2017,33(4):296-301.
[17]林媛,张树义,丛培根.渐近非扩张型映象具有误差的迭代收敛性[J].石河子大学学报(自然科学版),2017,35(4):517-513.
[18]Wang S.A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces[J].Applied Math Lett,2011,24:901-907.
[19]Shimizu T,Takahashi W.Strong convergence to common fixed points of families of nonexpansive mappings[J].J Math Anal Appl,1997,211(1):71-83.
[20]Suzuki T.Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals[J].J Math Anal Appl,2005,305(1):227-239.
[21]Liu L S.Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194(1):114-125.