scholarly journals An efficient iterative method for solving split variational inclusion problem with applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jamilu Abubakar ◽  
Poom Kumam ◽  
Abor Isa Garba ◽  
Muhammad Sirajo Abdullahi ◽  
Abdulkarim Hassan Ibrahim ◽  
...  
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Iterative Scheme ◽  
Variational Inclusion ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Monotone Mappings ◽  
Bounded Linear ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem

<p style='text-indent:20px;'>A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.</p>

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.

scholarly journals Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1037
Author(s):  
Bunyawee Chaloemyotphong ◽  
Atid Kangtunyakarn
Keyword(s):  
Iterative Method ◽  
Zero Point ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Numerical Example ◽  
Common Solution ◽  
Variational Inclusion Problem

The purpose of this paper is to introduce the split combination of variational inclusion problem which combines the concept of the modified variational inclusion problem introduced by Khuangsatung and Kangtunyakarn and the split variational inclusion problem introduced by Moudafi. Using a modified Halpern iterative method, we prove the strong convergence theorem for finding a common solution for the hierarchical fixed point problem and the split combination of variational inclusion problem. The result presented in this paper demonstrates the corresponding result for the split zero point problem and the split combination of variation inequality problem. Moreover, we discuss a numerical example for supporting our result and the numerical example shows that our result is not true if some conditions fail.

scholarly journals General Split Variational Inclusion Problem in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Yang ◽  
Fu Hai Zhao
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem

We consider a general split variational inclusion problem (GSFVIP) and propose an algorithm for finding the solutions of GSFVIP in Hilbert space. We establish the strong convergence of the proposed algorithm to a solution of GSFVIP. Our results extend and improve the related results in the literature.

scholarly journals Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 708 ◽  
Author(s):  
Suthep Suantai ◽  
Suparat Kesornprom ◽  
Prasit Cholamjiak
Keyword(s):  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Signal Recovery ◽  
Proximal Algorithms ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Lipschitz Constants ◽  
Theoretical Results

We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.

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