scholarly journals Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 273
Author(s):  
Mujahid Abbas ◽  
Muhammad Waseem Asghar ◽  
Manuel De la Sen
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Contraction Mapping ◽  
Iterative Scheme ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Examples ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Fractional Differential

The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme.

scholarly journals Common Fixed Points for Weak and Strong Convergence Results

2016 ◽  
Vol 4 (2) ◽  
pp. 340
Author(s):  
S. C. Shrivastava
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Results

<div><p> <em>In this paper, we study the approximation of common fixed points for more general classes of mappings through weak and strong convergence results of an iterative scheme in a uniformly convex Banach space. Our results extend and improve some known recent results.</em></p></div>

AN ITERATIVE SCHEME FOR FIXED POINT PROBLEMS

2021 ◽  
Vol 10 (5) ◽  
pp. 2295-2316
Author(s):  
F. Akutsah ◽  
O. K. Narain ◽  
K. Afassinou ◽  
A. A. Mebawondu
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Satisfying Condition ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Examples ◽  
Convergence Results ◽  
The Stability

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex Banach space. In addition, with the aid of numerical examples, we established that our newly proposed iterative scheme is faster than the iterative process introduced by Ullah et al., [26], Karakaya et al., [16], Abass et. al. [1] and some existing iterative scheme in literature. More so, the stability of our newly proposed iterative process is presented and we also gave some numerical examples to display the efficiency of our proposed algorithm.

scholarly journals Convergence results of a faster iterative scheme including multi-valued mappings in Banach spaces

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1359-1368
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Khan ◽  
Naseer Muhammad
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Current Literature ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Efficiency ◽  
Convergence Results

In this paper, we study M-iterative scheme in the new context of multi-valued generalized ?-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a new example of generalized ?-nonexpasive mappings. We connect M iterative scheme and other well known schemes with this example, to show the numerical efficiency of our results. Our results improve and extend many existing results in the current literature.

scholarly journals Iterative Algorithm for Mappings Satisfying Bγ,μ Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Iterative Algorithm ◽  
Iterative Algorithms ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Numerical Example ◽  
Strong And Weak Convergence ◽  
Convergence Results

In this article, we introduce a novel iterative algorithm to approximate fixed point of mappings with Bγ,μ condition. We establish some strong and weak convergence results in a uniformly convex Banach space. Using a numerical example, we compare the speed of the proposed algorithm with some leading iterative algorithms.

scholarly journals Inertial Iterative Schemes for D-Accretive Mappings in Banach Spaces and Curvature Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Li Wei ◽  
Wenwen Yue ◽  
Yingzi Shang ◽  
Ravi P. Agarwal
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Zero Point ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
New Techniques ◽  
Numerical Examples ◽  
Iterative Schemes ◽  
Uniformly Smooth ◽  
Accretive Mappings

We propose and analyze a new iterative scheme with inertial items to approximate a common zero point of two countable d-accretive mappings in the framework of a real uniformly smooth and uniformly convex Banach space. We prove some strong convergence theorems by employing some new techniques compared to the previous corresponding studies. We give some numerical examples to illustrate the effectiveness of the main iterative scheme and present an example of curvature systems to emphasize the importance of the study of d-accretive mappings.

scholarly journals A New Modified Fixed-Point Iteration Process

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3109
Author(s):  
Chanchal Garodia ◽  
Afrah A. N. Abdou ◽  
Izhar Uddin
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Fixed Point Iteration Process

In this paper, we present a new modified iteration process in the setting of uniformly convex Banach space. The newly obtained iteration process can be used to approximate a common fixed point of three nonexpansive mappings. We have obtained strong and weak convergence results for three nonexpansive mappings. Additionally, we have provided an example to support the theoretical proof. In the process, several relevant results are improved and generalized.

scholarly journals Convergence and stability of an iteration process and solution of a fractional differential equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohd Jubair ◽  
Faeem Ali ◽  
Javid Ali
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Iteration Process ◽  
Uniformly Convex ◽  
Nonlinear Fractional Differential Equation ◽  
Numerical Examples ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Fractional Differential ◽  
Condition C

AbstractIn this paper, we prove that a three-step iteration process is stable for contractive-like mappings. It is also proved analytically and numerically that the considered process converges faster than some remarkable iterative processes for contractive-like mappings. Furthermore, some convergence results are proved for the mappings satisfying Suzuki’s condition (C) in uniformly convex Banach spaces. A couple of nontrivial numerical examples are presented to support the main results and the visualization is showed by Matlab. Finally, by utilizing our main result the solution of a nonlinear fractional differential equation is approximated.

scholarly journals Estimation of Newly Established Iterative Scheme for Generalized Nonexpansive Mappings

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Aftab Hussain ◽  
Nawab Hussain ◽  
Danish Ali
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Space Environment ◽  
Iterative Approach ◽  
Uniformly Convex ◽  
Prior Art ◽  
Nonexpansive Maps ◽  
New Iterative Method

We introduce a new iterative method in this article, called the D iterative approach for fixed point approximation. Analytically, and also numerically, we demonstrate that our established D I.P is faster than the well-known I.P of the prior art. Finally, in a uniformly convex Banach space environment, we present weak as well as strong convergence theorems for Suzuki’s generalized nonexpansive maps. Our findings are an extension, refinement, and induction of several existing iterative literatures.

scholarly journals Convergence of Infinite Family of Multivalued Quasi-Nonexpansive Mappings Using Multistep Iterative Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Renu Chugh ◽  
Sanjay Kumar
Keyword(s):  
Real Banach Space ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Finite Family ◽  
Countable Family ◽  
Uniformly Convex ◽  
Iterative Schemes ◽  
Strong And Weak Convergence ◽  
Convergence Results

We prove strong and weak convergence results using multistep iterative sequences for countable family of multivalued quasi-nonexpansive mappings by using some conditions in uniformly convex real Banach space. The results presented extended and improved the corresponding result of Zhang et al. (2013), Bunyawat and Suantai (2012), and some others from finite family, one countable family, and two countable families tok-number of countable families of multivalued quasi-nonexpansive mappings. Also we used a numerical example in C++ computational programs to prove that the iterative scheme we used has better rate of convergence than other existing iterative schemes.

scholarly journals On Best Proximity Results for a Generalized Modified Ishikawa’s Iterative Scheme Driven by Perturbed 2-Cyclic Like-Contractive Self-Maps in Uniformly Convex Banach Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
M. De la Sen ◽  
Mujahid Abbas
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Convex Banach Space ◽  
The Self ◽  
Uniformly Convex ◽  
Cyclic Structure ◽  
Best Proximity Points ◽  
Uniformly Convex Banach Spaces

This paper proposes a generalized modified iterative scheme where the composed self-mapping driving can have distinct step-dependent composition order in both the auxiliary iterative equation and the main one integrated in Ishikawa’s scheme. The self-mapping which drives the iterative scheme is a perturbed 2-cyclic one on the union of two sequences of nonempty closed subsets Ann=0∞ and Bnn=0∞ of a uniformly convex Banach space. As a consequence of the perturbation, such a driving self-mapping can lose its cyclic contractive nature along the transients of the iterative process. These sequences can be, in general, distinct of the initial subsets due to either computational or unmodeled perturbations associated with the self-mapping calculations through the iterative process. It is assumed that the set-theoretic limits below of the sequences of sets Ann=0∞ and Bnn=0∞ exist. The existence of fixed best proximity points in the set-theoretic limits of the sequences to which the iterated sequences converge is investigated in the case that the cyclic disposal exists under the asymptotic removal of the perturbations or under its convergence of the driving self-mapping to a limit contractive cyclic structure.

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