On over-relaxed (A,η,m)-proximal point algorithm frameworks with errors and applications to general variational inclusion problems

نویسنده

  • Heng-you Lan
چکیده

The purpose of this paper is to provide some remarks for the main results of the paper Verma (Appl. Math. Lett. 21:142-147, 2008). Further, by using the generalized proximal operator technique associated with the (A,η,m)-monotone operators, we discuss the approximation solvability of general variational inclusion problem forms in Hilbert spaces and the convergence analysis of iterative sequences generated by the over-relaxed (A,η,m)-proximal point algorithm frameworks with errors, which generalize the hybrid proximal point algorithm frameworks due to Verma. MSC: 47H05; 49J40

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Graph Convergence for H(.,.)-co-Accretive Mapping with over-Relaxed Proximal Point Method for Solving a Generalized Variational Inclusion Problem

In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

متن کامل

Relaxed Proximal Point Algorithms Based on A−maximal Relaxed Monotonicity Frameworks with Applications

Based on the A−maximal (m)−relaxed monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems using the relaxed proximal point algorithm is explored, while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modified version of the relaxed proximal point algorithm, Eckstein and Bertsekas (1992) on weak conver...

متن کامل

Super-Relaxed (η)-Proximal Point Algorithms, Relaxed (η)-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions

We glance at recent advances to the general theory of maximal set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed η proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion ...

متن کامل

The Over-relaxed A−proximal Point Algorithm and Applications to Nonlinear Variational Inclusions in Banach Spaces

Based on the notion of A−maximal relaxed accretiveness, the convergence analysis of the over-relaxed proximal point algorithm in the context of the approximating the solutions of a class of nonlinear variational inclusions is explored. Moreover, some results on the general firm nonexpansiveness are also investigated. The obtained results are general and application-oriented in nature.

متن کامل

The Over-relaxed A−proximal Point Algorithm and Applications to Nonlinear Variational Inclusions in Banach Spaces

Based on the notion of A−maximal relaxed accretiveness, the convergence analysis of the over-relaxed proximal point algorithm in the context of the approximating the solutions of a class of nonlinear variational inclusions is explored. Moreover, some results on the general firm nonexpansiveness are also investigated. The obtained results are general and application-oriented in nature.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013