scholarly journals Nonlinear maximal monotone operators in Banach space

1968 ◽  
Vol 175 (2) ◽  
pp. 89-113 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Banach Space ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Nonlinear Maximal Monotone

scholarly journals Convergence theorems for generalized projections and maximal monotone operators in Banach spaces

2003 ◽  
Vol 2003 (10) ◽  
pp. 621-629 ◽  
Author(s):  
Takanori Ibaraki ◽  
Yasunori Kimura ◽  
Wataru Takahashi
Keyword(s):  
Banach Space ◽  
Pointwise Convergence ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convex Banach Space ◽  
Limit Set ◽  
Strong And Weak Convergence ◽  
Strictly Convex Banach Space ◽  
Generalized Projections

We study a sequence of generalized projections in a reflexive, smooth, and strictly convex Banach space. Our result shows that Mosco convergence of their ranges implies their pointwise convergence to the generalized projection onto the limit set. Moreover, using this result, we obtain strong and weak convergence of resolvents for a sequence of maximal monotone operators.

scholarly journals Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Somyot Plubtieng ◽  
Wanna Sriprad
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Convergence Rate ◽  
Minimization Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convex Minimization Problem ◽  
Mann Iteration ◽  
Strong And Weak Convergence

We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005).

Weak and Strong Convergence Theorems for Maximal Monotone Operators in a Banach Space

2004 ◽  
Vol 12 (4) ◽  
pp. 417-429 ◽  
Author(s):  
Shoji Kamimura ◽  
Fumiaki Kohsaka ◽  
Wataru Takahashi
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

scholarly journals Strong convergence of an iterative sequence for maximal monotone operators in a Banach space

2004 ◽  
Vol 2004 (3) ◽  
pp. 239-249 ◽  
Author(s):  
Fumiaki Kohsaka ◽  
Wataru Takahashi
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Iterative Sequence ◽  
Strong Convergence Theorem ◽  
Convex Minimization Problem ◽  
Proximal Point

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

scholarly journals Variational approach to nonlinear stochastic differential equations in Hilbert spaces

2021 ◽  
Vol 37 (2) ◽  
pp. 295-309
Author(s):  
VIOREL BARBU
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Variational Approach ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Existence Theory ◽  
Infinite Dimensional ◽  
Functional Methods ◽  
Nonlinear Maximal Monotone

Here we survey a few functional methods to existence theory for infinite dimensional stochastic differential equations of the form dX+A(t)X(t)=B(t,X(t))dW(t), X(0)=X_0, where A(t) is a non\-linear maximal monotone operator in a variational couple (V,V'). The emphasis is put on a new approach of the classical existence result of N. Krylov and B. Rozovski on existence for the infinite dimensional stochastic differential equations which is given here via the theory of nonlinear maximal monotone operators in Banach spaces. A variational approach to this problem is also developed.

scholarly journals A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yaqin Wang
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Fixed Points ◽  
Generalized Mixed Equilibrium Problem ◽  
Common Element ◽  
Strong Convergence Theorem

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.

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