Common Fixed Points of Two <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
                     <mi>G</mi>
                  </math>-Nonexpansive Mappings via a Faster Iteration Procedure

Khatoon, Sabiya; Uddin, Izhar; Ali, Javid; George, Reny

doi:10.1155/2021/9913540

Cited by 2 publications

(2 citation statements)

References 24 publications

(28 reference statements)

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“…Theorem 16. Suppose that the sequence fτ 1,n g is introduced by Picard (4), fτ 2,n g by Mann (5), fτ 3,n g by Ishikawa (6), fτ 4,n g by Noor (7), fτ 5,n g by Agrawal (8), and fτ n g by ( 9) iterative scheme which converges to the same point w. Then iterative scheme (9) converges faster than all the schemes (4)-( 8) to a fixed point of K.…”

Section: Convergence Results For Weak Contractionsmentioning

confidence: 99%

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Estimating Fixed Points via New Iterative Scheme with an Application

Jubair

Ali

Kumar

2022

Journal of Function Spaces

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In this paper, we introduce a new scheme and prove convergence results for nonexpansive mappings as well as for weak contractions in the frame of Banach spaces. Moreover, we prove analytically and numerically that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Further, we prove that the new scheme is almost stable with respect to weak contraction. For supporting the main results, we give a couple of nontrivial numerical examples, and the visualization is shown by using the Matlab program. Finally, the solution of a nonlinear fractional differential equation is approximated by operating the main result of the paper.

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Section: Convergence Results For Weak Contractionsmentioning

confidence: 99%

“…So, to overcome this kind of problem, several researchers constructed iterative schemes to approximate fixed points of mappings. A few of them are Picard-S [3], Thakur-New [4], and others [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Estimating Fixed Points via New Iterative Scheme with an Application

Jubair

Ali

Kumar

2022

Journal of Function Spaces

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Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

Chairatsiripong

Yambangwai

Thianwan

2023

Demonstratio Mathematica

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In this article, weak and strong convergence theorems of the M-iteration method for 𝒢-nonexpansive mapping in a uniformly convex Banach space with a directed graph were established. Moreover, weak convergence theorem without making use of Opial’s condition is proved. The rate of convergence between the M-iteration and some other iteration processes in the literature was also compared. Specifically, our main result shows that the M-iteration converges faster than the Noor and SP iterations. Finally, the numerical examples to compare convergence behavior of the M-iteration with the three-step Noor iteration and the SP-iteration were given. As application, some numerical experiments in real-world problems were provided, focused on image deblurring and signal recovering problems.

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Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure

Cited by 2 publications

References 24 publications

Estimating Fixed Points via New Iterative Scheme with an Application

Estimating Fixed Points via New Iterative Scheme with an Application

Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

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Common Fixed Points of Two G -Nonexpansive Mappings via a Faster Iteration Procedure

Cited by 2 publications

References 24 publications

Estimating Fixed Points via New Iterative Scheme with an Application

Estimating Fixed Points via New Iterative Scheme with an Application

Convergence analysis of M-iteration for 𝒢-nonexpansive mappings with directed graphs applicable in image deblurring and signal recovering problems

Contact Info

Product

Resources

About

Common Fixed Points of Two $G$ -Nonexpansive Mappings via a Faster Iteration Procedure