Shrinking hybrid method for multiple-sets split feasibility problems and variational inequality problems

2021 ◽  
Author(s):  
Maryam Safari ◽  
Fridoun Moradlou
Keyword(s):  
Variational Inequality ◽  
Hybrid Method ◽  
Variational Inequality Problems ◽  
Split Feasibility Problems ◽  
Split Feasibility

scholarly journals Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Panisa Lohawech ◽  
Anchalee Kaewcharoen ◽  
Ali Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Descent Method ◽  
Variational Inequality Problems ◽  
Steepest Descent Method ◽  
Split Feasibility Problems ◽  
The Common ◽  
Split Feasibility

In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.

scholarly journals Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2292
Author(s):  
Mujahid Abbas ◽  
Rizwan Anjum ◽  
Vasile Berinde
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Variational Inequality Problems ◽  
Iterative Approximation ◽  
Iteration Methods ◽  
Split Feasibility ◽  
Iteration Processes

The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

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