scholarly journals Iterative algorithm of common solutions for a constrained convex minimization problem, a quasi-variational inclusion problem and the fixed point problem of a strictly pseudo-contractive mapping

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Yifen Ke ◽  
Changfeng Ma
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Minimization Problem ◽  
Contractive Mapping ◽  
Fixed Point Problem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Convex Minimization Problem ◽  
Variational Inclusion Problem ◽  
Constrained Convex Minimization Problem

scholarly journals Solving Split Variational Inclusion Problem and Fixed Point Problem for Nonexpansive Semigroup without Prior Knowledge of Operator Norms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Haitao Che ◽  
Meixia Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Inclusion Problem ◽  
Point Problem ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Nonexpansive Semigroups ◽  
Operator Norms

We introduce an iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for nonexpansive semigroups with a way of selecting the stepsizes which does not need any prior information about the operator norms in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge strongly to a common element of the set of solutions of a split variational inclusion and the set of common fixed points of one-parameter nonexpansive semigroups. Moreover, numerical results demonstrate the performance and convergence of our result, which may be viewed as a refinement and improvement of the previously known results announced by many other researchers.

scholarly journals Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT(0) Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 749 ◽  
Author(s):  
Mujahid Abbas ◽  
Yusuf Ibrahim ◽  
Abdul Rahim Khan ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Multivalued Mappings ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Strictly Pseudocontractive Mapping ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem

The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in C A T ( 0 ) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of C A T ( 0 ) spaces.

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