Strong Convergence of Cesàro Mean Sequences and Split Equilibrium Solutions via Hybrid Mappings in Hilbert Spaces

Résumé

This paper introduces a novel accelerated shrinking projection algorithm for approximating Cesàro mean sequences and solving split equilibrium problems in real Hilbert spaces. The iterative scheme is constructed using finite families of commutative, normally m-generalized hybrid mappings, with a step size chosen independently of the spectral radius to facilitate computation. We prove that the generated sequence converges strongly to a common element in the intersection of the fixed point sets of the mappings, which also solves the associated split equilibrium problem. The proposed method yields new and extended strong convergence theorems for various classes of hybrid mappings, including normally generalized hybrid, m-generalized hybrid, and normally 2-generalized hybrid mappings. A numerical example is provided to demonstrate the superior convergence rate of our algorithm compared to existing methods. These results generalize and unify several known findings in this direction.

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