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

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
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Mathematics 2019, 7(11), 1037; https://doi.org/10.3390/math7111037
Received: 29 August 2019 / Revised: 28 October 2019 / Accepted: 29 October 2019 / Published: 3 November 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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. View Full-Text
Keywords: split variational inclusion problem; hierarchical fixed point problem; fixed point problem split variational inclusion problem; hierarchical fixed point problem; fixed point problem
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Chaloemyotphong, B.; Kangtunyakarn, A. Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space. Mathematics 2019, 7, 1037.

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