多输出集分裂公共不动点问题的强收敛方法

Strongly convergent methods for the split common fixed point problem with multiple output sets

摘要

本文针对半压缩算子族的多输出集分裂公共不动点问题,提出了新型多步交替惯性迭代算法,并且在适当条件下建立了该算法生成序列的强收敛定理.该算法融合了多步惯性加速技术与自适应步长策略,使其能够灵活应对不同计算的场景,提升迭代的稳定性与收敛效率.

Abstract

This paper proposes a novel multi-step alternating inertial iterative algorithm for the split common fixed point problem with multiple-output sets of a family of demi-contractive operators. Under appropriate conditions, a strong convergence theorem for the sequence generated by this algorithm is established. The algorithm integrates multi-step inertial acceleration techniques with an adaptive stepsize strategy, enabling it to flexibly adapt to various computational scenarios and enhance iterative stability and convergence efficiency.

关键词

不动点 / 半压缩映射 / 半闭性

Key words

fixed point / demi-contractive mapping / demiclosedness

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基金资助

河南省杰出青年科学基金(252300421057)

河南省高校科技创新团队(26IRTSTHN024)

国家自然科学基金(11971216)

河南省高等学校重点科研项目(26A1100130)