scholarly journals The p-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with (A,η)-accretive operators in q-uniformly smooth banach spaces

2008 ◽  
Vol 220 (1-2) ◽  
pp. 163-174 ◽  
Author(s):  
Xie Ping Ding ◽  
Hai Rong Feng
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Variational Inclusions ◽  
Accretive Operators ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

scholarly journals System of Multi-Valued Mixed Variational Inclusions with XOR-Operation in Real Ordered Uniformly Smooth Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1027
Author(s):  
Rais Ahmad ◽  
Imran Ali ◽  
Xiao-Bing Li ◽  
Mohd. Ishtyak ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Variational Inclusions ◽  
Uniformly Smooth ◽  
Xor Operation ◽  
Uniformly Smooth Banach Spaces

In this paper, we consider and study a system of multi-valued mixed variational inclusions with XOR-operation ⊕ in real ordered uniformly smooth Banach spaces. This system consists of bimappings, multi-valued mappings and Cayley operators. An iterative algorithm is suggested to find the solution to a system of multi-valued mixed variational inclusions with XOR-operation ⊕ and consequently an existence and convergence result is proved. In support of our main result, an example is constructed.

MODIFIED HALPERN ITERATIVE ALGORITHM FOR NONEXPANSIVE MAPPINGS II

2011 ◽  
Vol 04 (04) ◽  
pp. 683-694
Author(s):  
Mengistu Goa Sangago
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Convergence Conditions ◽  
Uniformly Smooth ◽  
Additional Control ◽  
Uniformly Smooth Banach Spaces

Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Yao et al. [16] modification of Halpern iterative algorithm for nonexpansive mappings in uniformly smooth Banach spaces. Unfortunately, some deficiencies are found in the Yao et al. [16] control conditions imposed on the modified iteration to obtain strong convergence. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Yao et al. [16] are not sufficient and it is also proved that with some additional control conditions on the parameters strong convergence of the iteration is obtained.

scholarly journals Approximating the zeros of accretive operators by the Ishikawa iteration process

1996 ◽  
Vol 1 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Zhou Haiyun ◽  
Jia Yuting
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Process ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Uniformly Smooth ◽  
Ishikawa Iteration Process ◽  
Uniformly Smooth Banach Spaces ◽  
Iteration Processes

Some strong convergence theorems are established for the Ishikawa iteration processes for accretive operators in uniformly smooth Banach spaces.

scholarly journals Resolvent operator technique for solving a system of generalized variational-like inclusions in Banach spaces

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 897-908
Author(s):  
Rais Ahmad ◽  
Mohammad Dilshad ◽  
Mohammad Akram
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Existence Of Solutions ◽  
Operator Technique ◽  
Uniformly Smooth ◽  
Resolvent Operator Technique ◽  
Uniformly Smooth Banach Spaces ◽  
Matlab Programming ◽  
Cocoercive Operator

In this paper, we apply H(?,?)-?-cocoercive operator introduced in [2] for solving a system of generalized variational-like inclusions in q-uniformly smooth Banach spaces. By using the approach of resolvent operator associated with H(?,?)-?-cocoercive operator, an iterative algorithm for solving a system of generalized variational-like inclusions is constructed. We prove the existence of solutions of system of generalized variational-like inclusions and convergence of iterative sequences generated by the algorithm. An example through Matlab programming is constructed.

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