1. Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space
- Author
-
Atid Kangtunyakarn and Bunyawee Chaloemyotphong
- Subjects
021103 operations research ,Iterative method ,fixed point problem ,General Mathematics ,split variational inclusion problem ,lcsh:Mathematics ,0211 other engineering and technologies ,Hilbert space ,Zero-point energy ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,hierarchical fixed point problem ,010101 applied mathematics ,symbols.namesake ,Fixed point problem ,Convergence (routing) ,Computer Science (miscellaneous) ,symbols ,Applied mathematics ,Inequality problem ,0101 mathematics ,Engineering (miscellaneous) ,Mathematics - Abstract
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.
- Published
- 2019