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<p>In this paper, we suggest and analyze a noval iterative method based on Mann and Halpern iterative method to find a common solution of split null point problem, split mixed equilibrium problem and fixed point problem for a nonexpansive mapping in real Hilbert spaces. Further, by employing the properties of monotone operators, equilibrium bifunctions, and nonexpansive mappings, we establish strong convergence results under mild and standard assumptions. Our approach generalizes and unifies several existing iterative methods in the literature, and numerical examples are presented to demonstrate the effectiveness and applicability of the proposed algorithm.</p>

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A Mann-Halpern algorithm for solving split null point, split mixed equilibrium and fixed point problems for a nonexpansive mapping

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Shuja Haider Rizvi

摘要

In this paper, we suggest and analyze a noval iterative method based on Mann and Halpern iterative method to find a common solution of split null point problem, split mixed equilibrium problem and fixed point problem for a nonexpansive mapping in real Hilbert spaces. Further, by employing the properties of monotone operators, equilibrium bifunctions, and nonexpansive mappings, we establish strong convergence results under mild and standard assumptions. Our approach generalizes and unifies several existing iterative methods in the literature, and numerical examples are presented to demonstrate the effectiveness and applicability of the proposed algorithm.