Journal of Fixed Point Theory and Applications· 2026Q2
Generating Halpern-type iterative schemes to solve fixed point and null point problems
- 0citations
- Q2SCImago
- 2026year
Short summary
Three new iterative scheme generating methods (ISGMs) produce infinitely many Halpern-type strong convergence theorems, improving upon prior weak convergence results for nonlinear mappings and enabling approximation of null points for maximal monotone mappings.
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Key points
- Introduced three types of iterative scheme generating methods (ISGMs).
- Developed Halpern-type strong convergence theorems for nonlinear mappings.
- Exploited resolvents to approximate null points of maximal monotone multi-valued mappings.
- Presented a mixed-type result solving both fixed point and null point problems simultaneously.
AI-generated from the title and abstract; the full text is not read.
Abstract
This study establishes three types of iterative scheme generating methods (ISGMs), each of which yields infinitely many Halpern-type strong convergence theorems. The first result strengthens the previous Mann-type result that guarantees only weak convergence to common fixed points of nonlinear mappings. Next, we exploit resolvents for approximating null points of maximal monotone multi-valued mappings. A mixed-type result is also presented, which simultaneously solves fixed point and null point problems. We explicitly present several variations of iterative schemes derived from the main theorems, including multi-step iterative methods. We also study iterative methods for solving split common null point problems, as applications.
The authors' abstract, as published at the source. Journal of Fixed Point Theory and Applications, 2026 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics