Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces

• الحاوية / القاعدة: Journal of Inequalities and Applications
• المؤلفون الرئيسيون: Jinhua Zhu, Jinfang Tang, Shih-sen Chang
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: SpringerOpen 2018-10-01
• الموضوعات: Split feasibility; Maximal monotone operators; Inverse strongly monotone operator; Fixed point problems; Strong convergence theorems
• الوصول للمادة أونلاين: http://link.springer.com/article/10.1186/s13660-018-1881-x
• تدمد: 1029-242X

Abstract In this paper we consider a class of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces. One of them is the set of zero points of the sum of two monotone operators and the other is the set of fixed points of mappings. By using the modified forward–backward splitting method, we propose a viscosity iterative algorithm. Under suitable conditions, some strong convergence theorems of the sequence generated by the algorithm to a common solution of the problem are proved. At the end of the paper, some applications and the constructed algorithm are also discussed.