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<p>We study the iterative scheme given by a sequence of nonexpansive (firmly nonexpansive, contractive) self-mappings of a nonempty closed convex subset of a real Hilbert space. We establish some ergodic convergence, almost convergence and convergence results of the generated sequence for both the weak and the strong topologies. Our motivations are unification of some iterative schemes, stability of ergodic convergence with respect to the nonexpansive mapping and the study of non-autonomous evolutions of nonexpansive mappings.</p>

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Some convergence theorems for a sequence of nonexpansive mappings in a Hilbert space

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Ali Yousefi Pirbasti,
  • Hadi Khatibzadeh,
  • Mohsen Rahimi Piranfar

摘要

We study the iterative scheme given by a sequence of nonexpansive (firmly nonexpansive, contractive) self-mappings of a nonempty closed convex subset of a real Hilbert space. We establish some ergodic convergence, almost convergence and convergence results of the generated sequence for both the weak and the strong topologies. Our motivations are unification of some iterative schemes, stability of ergodic convergence with respect to the nonexpansive mapping and the study of non-autonomous evolutions of nonexpansive mappings.