Equivalence between iterative schemes in modular spaces

Abed, Salwa Salman; Abduljabbar, Meena Fouad

doi:10.1080/09720502.2019.1706850

Cited by 8 publications

(6 citation statements)

References 8 publications

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“…We suggest studying this algorithm for two finite families of the general asymptotic set-valued mappings. In [18], there is a study for Fibonacci-Mann random scheme of a monotone asymptotically nonexpansive random operators. We suggest an analogous study for the mappings in (1.5).…”

Section: Open Problemmentioning

confidence: 99%

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

Abed¹

2020

JAM

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The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by yn+1 = tn z+ (1-tn )un , un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

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Section: Open Problemmentioning

confidence: 99%

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

Abed¹

2020

JAM

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“…It was then redefined with some modification by Musielak and Ortiz in 1959 In 2017, the best approximation modular spaces have been defined by Abed 8 and results about proximinal set, Chebysev set are proven also, see 9 . Various results in modular spaces and other related spaces about fixed point problem can be seen in Turkoglu and Nesrin 9 , Albundi 10 , Abdul Jabbar and Abed 11,12 , Ahmed 13 , Mohammed and Abed 14 , Pathak and Beg 15 , Abed and Abdul Jabbar 16,17 , Ege and, Alac 18 also Abed and Salman 19 .…”

Section: Introductionmentioning

confidence: 99%

افضل تقريب في فضاءات b - المعيارية

Jabbar,

Kadhim,

Abed

2024

Baghdad Sci.J

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In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given. For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

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“…Then, a few of its characteristics have emerged, enabling the handling of outcomes connected to the idea of uniformly smooth convex real modular spaces. In this regards, Abed and Abduljabbar [16] demonstrated convergence for iteration algorithms in multivalued mappings in modular function spaces. Using the Picard-Krasnoselskii hybrid iterative process in these spaces, Okeke et al [17] proved theorems for -quasi-nonexpansive mappings.…”

Section: Introductionmentioning

confidence: 99%

A New Iterative Sequence of (λ, ρ)-Firmly Nonexpansive Multi-Valued Mappings in Modular Function Spaces with Applications

Salman¹,

Abed²

2023

MMEP

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The fixed point theory is of great importance as it is used as an application for solving differential equations for different types of equations and various applications in physical, engineering, and statistical sciences. This investigation aims to define (λ, ρ)firmly nonexpansive multivalued mappings in modular function spaces and to introduce a new iterative algorithm. Accordingly, some results of approximating fixed points for these mappings are proved with an example. Further, the concept of stability is discussed and supported by an example.

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Equivalence between iterative schemes in modular spaces

Cited by 8 publications

References 8 publications

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

افضل تقريب في فضاءات b - المعيارية

A New Iterative Sequence of (λ, ρ)-Firmly Nonexpansive Multi-Valued Mappings in Modular Function Spaces with Applications

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