scholarly journals A modification of the forward-backward splitting method for maximal monotone mappings

2013 ◽  
Vol 3 (2) ◽  
pp. 295-307 ◽  
Author(s):  
Xiao Ding ◽  
◽  
Deren Han
Keyword(s):  
Splitting Method ◽  
Maximal Monotone ◽  
Monotone Mappings ◽  
Maximal Monotone Mappings

Explicit algorithms for J-fixed points of some non linear mappings in certain Banach spaces

2020 ◽  
Vol 29 (1) ◽  
pp. 27-36
Author(s):  
M. M. GUEYE ◽  
M. SENE ◽  
M. NDIAYE ◽  
N. DJITTE
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Maximal Monotone ◽  
Point Theory ◽  
Duality Mapping ◽  
Monotone Mappings ◽  
Normalized Duality Mapping ◽  
Maximal Monotone Mappings ◽  
Pseudocontractive Mappings

Let E be a real normed linear space and E∗ its dual. In a recent work, Chidume et al. [Chidume, C. E. and Idu, K. O., Approximation of zeros of bounded maximal monotone mappings, solutions of hammerstein integral equations and convex minimizations problems, Fixed Point Theory and Applications, 97 (2016)] introduced the new concepts of J-fixed points and J-pseudocontractive mappings and they shown that a mapping A : E → 2 E∗ is monotone if and only if the map T := (J −A) : E → 2 E∗ is J-pseudocontractive, where J is the normalized duality mapping of E. It is our purpose in this work to introduce an algorithm for approximating J-fixed points of J-pseudocontractive mappings. Our results are applied to approximate zeros of monotone mappings in certain Banach spaces. The results obtained here, extend and unify some recent results in this direction for the class of maximal monotone mappings in uniformly smooth and strictly convex real Banach spaces. Our proof is of independent interest.

scholarly journals Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 547828
Author(s):  
Yuan Qing ◽  
Xiaolong Qin ◽  
Haiyun Zhou ◽  
ShinMin Kang
Keyword(s):  
Hilbert Spaces ◽  
Maximal Monotone ◽  
Monotone Mappings ◽  
Maximal Monotone Mappings

scholarly journals A note on Solodov and Tseng’s methods for maximal monotone mappings

2010 ◽  
Vol 234 (5) ◽  
pp. 1522-1527
Author(s):  
Jinling Zhao ◽  
Qingzhi Yang ◽  
Hongxiu Gao
Keyword(s):  
Maximal Monotone ◽  
Monotone Mappings ◽  
Maximal Monotone Mappings
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