System of variational inclusions with ${(\emph{\textbf{H}},{\bm\phi})}$-$\bm\eta$-monotone operators in Banach spaces
-
摘要: 在实的一致光滑Banach空间中, 引入一类新的含$(H,\phi)$-$\eta$-单调算子的变分包含组. 利用$(H,\phi)$-$\eta$-单调算子的近似映射技巧, 证明了此类新的变分包含组解的存在性与唯一性, 并构造了逼近此类变分包含组解 的迭代算法; 讨论了由此迭代算法生成的迭代序列的收敛性. 所得结果推广与改进了文献中的一些主要结果.
-
关键词:
- $(H,\phi)$-$\eta$-单调算子 /
- 近似映射 /
- 变分包含组 /
- 迭代算法 /
- 收敛性
Abstract: This paper introduced a new system of variational inclusions with $(H,\phi)$-$\eta$-monotone operators in real uniformly smooth Banach spaces. By using the proximal mapping technique associated with $(H,\phi)$-$\eta$-monotone operators, we proved the existence and uniqueness of solution for this new system and construct a new iterative algorithm for approximating the solution of this system. The convergence of the iterative sequence generated by the iterative algorithm was also discussed. The results extend and improve some known results in the literature. -
[1] {1}ZENG L C, GUU S M, YAO J C. Characterization of $H$-monotoneoperators with applications to variational inclusions[J]. ComputMath Appl, 2005, 50: 329-337.{2}LAN H Y, KIM J H, CHO Y J. On a new system of nonlinear $A$-monotonemulti-valued variational inclusions[J]. J Math Anal Appl, 2007, 327:481-493.{3}VERMA R U. $A$-monotonicity and applications to nonlinear inclusionproblems[J]. J Appl Math Stochastic Anal, 2004, 17(2): 193-195.{4}VERMA R U. Generalized nonlinear variational inclusion problemsinvolving $A$-monotone mappings[J]. Appl Math Lett, 2006, 19(9):960-963.{5}XIA F Q, HUANG N J. Variational inclusions with a general$H$-monotone operator in Banach spaces[J]. Comput Math Appl, 2007,54(1): 24-30.{6}DING X P, FENG H R. Algorithm for solving a new class of generalizednonlinear implicit qusi-variational inclusions in Banach spaces[J].Appl Math Comput, 2009, 208(2): 547-555.{7}FENG H R, DING X P. A new system of generalized nonlinearquasi-variational-like inclusions with $A$-monotone operators inBanach spaces[J]. J Comput Appl Math, 2009, 225(2): 365-373.{8}LOU J, HE X F, HE Z. Iterative methods for solving a system ofvariational inclusions involving $H$-$\eta$-monotone operators inBanach spaces[J]. Comput Math Appl, 2008, 55(7): 1832-1841.{9}DING X P, WANG Z B. System of set-valued mixedquasi-variational-like inclusions involving $H$-$\eta$-monotoneoperators in Banach spaces[J]. Appl Math Mech, 2009, 30(1): 1-12.{10}VERMA R U. Approximation solvability of a class of nonlinearset-valued inclusions involving $(A, \eta)$-monotone mappings[J]. JMath Anal Appl, 2008, 337(2): 969-975.{11}FANG Y P, HUANG N J, Thompson H B. A new system of variationalinclusions with $(H, \eta)$-monotone operators in Hilbert spaces[J].J Comput Math Appl, 2005, 49: 365-374.{12}FANG Y P, HUANG N J. $H$-monotone operator and systems ofvariational inclusions[J]. Commun Appl Nonlinear Anal, 2004, 11(1):93-101.{13}FANG Y P, HUANG N J. $H$-monotone operator and resolvent operatortechnique for variational inclusions[J]. Appl Math Comput, 2003,145(2-3): 795-803.{14}LUO X P, HUANG N J. A new class of variational inclusions with$B$-monotone operators in Banach spaces[J]. J Comput Appl Math,2010, 233(8): 1888-1896.{15}PETERSHYN W V. A characterization of strictly convexity of Banachspaces and other uses of duality mappings[J]. J Funct Anal, 1970, 6:282-291.{l6}LUO X P, HUANG N J. $(H, \phi)$-$\eta$-monotone operators in Banachspaces with an application to variational inclusions[J]. Appl MathComput, 2010, 216(4): 1131-1139.{17}HUANG N J, FANG Y P. A new class of general variational inclusionsinvolving maximal $\eta$-monotone mappings[J]. Publ Math Debrecen,2003, 62(1-2): 83-98.
点击查看大图
计量
- 文章访问数: 2771
- HTML全文浏览量: 21
- PDF下载量: 2102
- 被引次数: 0