scholarly journals The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 560 ◽  
Author(s):  
Pawicha Phairatchatniyom ◽  
Poom Kumam ◽  
Yeol Je Cho ◽  
Wachirapong Jirakitpuwapat ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Fixed Point ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Inclusion Problem ◽  
Common Elements ◽  
Inclusion Problems ◽  
Variational Inclusion Problem ◽  
Inertial Extrapolation ◽  
Appl Math

Based on the very recent work by Shehu and Agbebaku in Comput. Appl. Math. 2017, we introduce an extension of their iterative algorithm by combining it with inertial extrapolation for solving split inclusion problems and fixed point problems. Under suitable conditions, we prove that the proposed algorithm converges strongly to common elements of the solution set of the split inclusion problems and fixed point problems.

scholarly journals A modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
pp. 28-39
Author(s):  
Thierno M. M. Sow
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Proximal Point Algorithm ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Proximal Point ◽  
Inclusion Problems ◽  
Common Solution ◽  
Variational Inclusion Problem ◽  
The Common

AbstractThe purpose of this paper is to use a modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces. It is proven that the sequence generated by the proposed iterative algorithm converges strongly to the common solution of the convex minimization and variational inclusion problems.

scholarly journals Weak and strong convergence of inertial algorithms for solving split common fixed point problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong-Yi Chen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Linear Operators ◽  
Fixed Point Problems ◽  
Inclusion Problem ◽  
Mann Iteration ◽  
Contractive Mappings ◽  
Variational Inclusion Problem ◽  
Split Common Fixed Point

AbstractIn this paper, we propose two iterative schemes for approximating solutions of split common fixed point problems in multiple linear operators case. The first algorithm implements the Krasnosel’skiĭ–Mann iteration with an inertial effect for which the weak convergence is established under mild assumptions. With the tool of nearly contractive mappings, we introduce a viscosity-type iteration which ensures strong convergence. We apply our results to solve a multiple split monotone variational inclusion problem. A numerical example is given to demonstrate the efficiency of the proposed algorithms.

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