scholarly journals Hybrid iterative algorithms for two families of finite maximal monotone mappings

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Yang-Qing Qiu ◽  
Lu-Chuan Ceng ◽  
Jin-Zuo Chen ◽  
Hui-Ying Hu
Keyword(s):  
Maximal Monotone ◽  
Iterative Algorithms ◽  
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 Completely generalized multivalued nonlinear quasi-variational inclusions

2002 ◽  
Vol 30 (10) ◽  
pp. 593-604 ◽  
Author(s):  
Zeqing Liu ◽  
Lokenath Debnath ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Existence Theorems ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Monotone Mappings ◽  
Operator Technique ◽  
Variational Inclusions ◽  
New Class ◽  
Convergence Results ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.

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
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