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Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings

Author

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  • Jong Soo Jung

    (Department of Mathematics, Dong-a University, Busan 49315, Korea)

Abstract

In this paper, first, we introduce a path for a convex combination of a pseudocontractive type of mappings with a perturbed mapping and prove strong convergence of the proposed path in a real reflexive Banach space having a weakly continuous duality mapping. Second, we propose two modified implicit iterative methods with a perturbed mapping for a continuous pseudocontractive mapping in the same Banach space. Strong convergence theorems for the proposed iterative methods are established. The results in this paper substantially develop and complement the previous well-known results in this area.

Suggested Citation

  • Jong Soo Jung, 2020. "Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings," Mathematics, MDPI, vol. 8(1), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:72-:d:304699
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