Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

Agwu, Imo Kalu; Igbokwe, Donatus Ikechi; Ukeje, Nathenial C.

doi:10.28924/ada/ma.1.45

Eur. J. Math. Anal.

2021

DOI: 10.28924/ada/ma.1.45

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Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

Imo Kalu Agwu¹,

Donatus Ikechi Igbokwe²,

Nathenial C. Ukeje³

Abstract: We propose a three-step iteration scheme of hybrid mixed-type for three total asymptotically nonexpansive self mappings and three total asymptotically nonexpansive nonself mappings. In addition, we establish some weak convergence theorems of the scheme to the common fixed point of the mappings in uniformly convex Banach spaces. Our results extend and generalize numerous results currently in literature.

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Cited by 2 publications

References 8 publications

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A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces

Saleem,

Kalu Agwu,

Ishtiaq

et al. 2023

Journal of Mathematics

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In this paper, firstly, we introduce a method for finding common fixed point of L -Lipschitzian and total asymptotically strictly pseudo-non-spreading self-mappings and L -Lipschitzian and total asymptotically strictly pseudo-non-spreading non-self-mappings in the setting of a real uniformly convex Banach space. Secondly, the demiclosedness principle for total asymptotically strictly pseudo-non-spreading non-self-mappings is established. Thirdly, the weak convergence theorems of the proposed method to the common fixed point of the above mappings are proved. Our results improved, extended, and generalized some corresponding results in the literature.

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A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces

Saleem,

Kalu Agwu,

Ishtiaq

et al. 2023

Journal of Mathematics

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Strong and Weak Convergence Theorems for the Split Feasibility Problem of (β,k)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces

Razzaque,

Saleem,

Agwu

et al. 2024

Symmetry

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The concept of symmetry has played a major role in Hilbert space setting owing to the structure of a complete inner product space. Subsequently, different studies pertaining to symmetry, including symmetric operators, have investigated real Hilbert spaces. In this paper, we study the solutions to multiple-set split feasibility problems for a pair of finite families of β-enriched, strictly pseudocontractive mappings in the setup of a real Hilbert space. In view of this, we constructed an iterative scheme that properly included these two mappings into the formula. Under this iterative scheme, an appropriate condition for the existence of solutions and strong and weak convergent results are presented. No sum condition is imposed on the countably finite family of the iteration parameters in obtaining our results unlike for several other results in this direction. In addition, we prove that a slight modification of our iterative scheme could be applied in studying hierarchical variational inequality problems in a real Hilbert space. Our results improve, extend and generalize several results currently existing in the literature.

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Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

Cited by 2 publications

References 8 publications

A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces

A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces

Strong and Weak Convergence Theorems for the Split Feasibility Problem of (β,k)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces

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