A perturbed algorithm for a system of variational inclusions involving H(·, ·)-accretive operators in Banach spaces

In this paper, using the properties of graph convergence of H(@?,@?)-accretive operators, we construct a perturbed algorithm for solving systems of ill-posed variational inclusions involving H(@?,@?)-accretive operators. Under some suitable conditions, we prove that the sequence generated by the proposed method is strongly convergent to the unique solution of the problem. The main results presented in this paper generalize and improve some recent results in the literature.

[1]  Qamrul Hasan Ansari,et al.  An iterative algorithm for generalized nonlinear variational inclusions , 2000, Appl. Math. Lett..

[2]  H. Attouch.  Variational convergence for functions and operators , 1984 .

[3]  Nan-jing Huang,et al.  Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions , 1998 .

[4]  Nan-jing Huang,et al.  Generalized nonlinear variational inclusions with noncompact valued mappings , 1996 .

[5]  Hong-Kun Xu.  Inequalities in Banach spaces with applications , 1991 .

[6]  Li-Wei Liu,et al.  On generalized set-valued variational inclusions , 2001 .

[7]  N. Huang,et al.  A new system of variational inclusions with (H, η )-monotone operators in hilbert spaces , 2005 .

[8]  Daoli Zhu,et al.  A new system of generalized mixed quasi-variational inclusions with (H,η)-monotone operators☆ , 2007 .

[9]  R. Verma.  A system of generalized auxiliary problems principle and a system of variational inequalities , 2001 .

[10]  Dao Li Zhu,et al.  A system of variational inclusions with P-η-accretive operators , 2008 .

[11]  Jen-Chih Yao,et al.  A perturbed algorithm for strongly nonlinear variational-like inclusions , 2000, Bulletin of the Australian Mathematical Society.

[12]  NOTES ON GRAPH-CONVERGENCE FOR MAXIMAL MONOTONE OPERATORS , 2011 .

[13]  Xie Ping Ding,et al.  A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces , 2009 .

[14]  Nan-Jing Huang,et al.  H(*, *)-accretive operator with an application for solving variational inclusions in Banach spaces , 2008, Appl. Math. Comput..

[15]  Nan-Jing Huang,et al.  A new system of variational inclusions involving H(*, *)-accretive operator in Banach spaces , 2009, Appl. Math. Comput..

[16]  Nan-Jing Huang,et al.  An existence result for a system of inclusion problems with applications , 2008, Appl. Math. Lett..

[17]  Ram U. Verma,et al.  General nonlinear variational inclusion problems involving A-monotone mappings , 2006, Appl. Math. Lett..

[18]  Yeol Je Cho,et al.  Nonlinear relaxed cocoercive variational inclusions involving (A, eta)-accretive mappings in banach spaces , 2006, Comput. Math. Appl..

[19]  Kaleem Raza Kazmi,et al.  Mann and Ishikawa Type Perturbed Iterative Algorithms for Generalized Quasivariational Inclusions , 1997 .

[20]  G. W. Reddien,et al.  Projection Methods , 2021, Introduction to the Numerical Solution of Markov Chains.

[21]  Xie Ping Ding,et al.  A new class of completely generalized quasi-variational inclusions in Banach spaces , 2002 .

[22]  Samir Adly,et al.  Perturbed algorithms and sensitivity analysis for a general class of variational inclusions , 1996 .

[23]  Abul Hasan Siddiqi,et al.  A Perturbated Algorithm for Generalized Nonlinear Quasi-Variational Inclusions , 1998 .

[24]  Nan-jing Huang,et al.  A new completely general class of variational inclusions with noncompact valued mappings , 1998 .

[25]  N. Huang,et al.  Generalized H-η-accretive operators in Banach spaces with application to variational inclusions , 2010 .

[26]  József Kolumbán,et al.  Factorization of Minty and Stampacchia variational inequality systems , 2002, Eur. J. Oper. Res..

[27]  Shin Min Kang,et al.  Convergence and stability of perturbed three-step iterative algorithm for completely generalized nonlinear quasivariational inequalities , 2004, Appl. Math. Comput..

[28]  Nan-Jing Huang,et al.  H-Accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces , 2004, Appl. Math. Lett..

[29]  Nan-Jing Huang,et al.  A new class of variational inclusions with B-monotone operators in Banach spaces , 2010, J. Comput. Appl. Math..

[30]  Xie Ping Ding,et al.  (H(., .), eta)-accretive operators with an application for solving set-valued variational inclusions in Banach spaces , 2010, Comput. Math. Appl..

[31]  R. U. Verma,et al.  Sensitivity analysis for generalized strongly monotone variational inclusions based on the (A, eta)-resolvent operator technique , 2006, Appl. Math. Lett..

[32]  Jen-Chih Yao,et al.  Systems of generalized variational inequalities and their applications , 2000 .

[33]  Jen-Chih Yao,et al.  A fixed point theorem and its applications to a system of variational inequalities , 1999, Bulletin of the Australian Mathematical Society.

[34]  Zsolt Páles,et al.  On Nash stationary points , 1999, Publicationes Mathematicae Debrecen.

[35]  Ya-Ping Fang,et al.  H-Monotone operator and resolvent operator technique for variational inclusions , 2003, Appl. Math. Comput..

[36]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[37]  Abul Hasan Siddiqi,et al.  General strongly nonlinear variational inequalities , 1992 .

[38]  Xi Li,et al.  Graph convergence for the H(·, ·)-accretive operator in Banach spaces with an application , 2011, Appl. Math. Comput..

[39]  Nan-Jing Huang,et al.  Iterative algorithm for a system of variational inclusions involving H-accretive operators in Banach spaces , 2005 .