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Open AccessArticle

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

Department of Mathematics, Dong-a University, Busan 49315, Korea
Mathematics 2020, 8(1), 72; https://doi.org/10.3390/math8010072
Received: 14 October 2019 / Revised: 24 December 2019 / Accepted: 26 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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. View Full-Text
Keywords: modified implicit iterative methods with perturbed mapping; pseudocontractive mapping; strongly pseudocontractive mapping; nonexpansive mapping; weakly continuous duality mapping; fixed point modified implicit iterative methods with perturbed mapping; pseudocontractive mapping; strongly pseudocontractive mapping; nonexpansive mapping; weakly continuous duality mapping; fixed point
MDPI and ACS Style

Jung, J.S. Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings. Mathematics 2020, 8, 72.

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