A new fixed point algorithm for finding the solution of a delay differential equation

The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Also, we show that our proposed iterative algorithm converges weakly and strongly to the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Furthermore, it is proved analytically that our new iterative algorithm converges faster than one of the leading iterative algorithms in the literature for almost contraction mappings. Some numerical examples are also provided and used to show that our new iterative algorithm has better rate of convergence than all of S, Picard-S, Thakur and M iterative algorithms for almost contraction mappings and generalized α-nonexpansive mappings. Again, we show that the proposed iterative algorithm is stable with respect to T and data dependent for almost contraction mappings. Some applications of our main results and new iterative algorithm are considered. The results in this article are improvements, generalizations and extensions of several relevant results existing in the literature.

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“…Thakur [36], Thakur New [37], M [39], M* [38], Garodia and Uddin [16], Two-Step Mann [35] iterative algorithms and many others.…”

mentioning

confidence: 99%

New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

Ofem¹,

Udofia²,

Igbokwe³

2021

Eur. J. Math. Anal.

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“…A nontrivial example of a nonlinear Volterra delay integro-differential equation which satisfies all the mild conditions used in obtaining our result has been provided. We have also seen that the class of delay differential equation studied in [4,9,12,23,[25][26][27] is a special case of the class nonlinear Volterra delay integro-differential equation considered in this article. Hence, our results generalize, improve and unify the corresponding results in [4,9,12,15,[23][24][25][26][27][28] and several others in the existing literature.…”

Section: Discussionmentioning

confidence: 85%

“…x(t) = ψ(t), t ∈ [−r, 0], (6.10) which is the initial value problem for a nonlinear Volterra integro-differential equation. The approximation of solution the problem (6.9)-(6.10) has been studied by several authors for ℘ 1 (t, s, x(s), x(t − r)) = 0 (see for example [4,9,12,23,[25][26][27] and the references there in). Hence, our result in Theorem 8 generalizes the corresponding results in [4,9,12,23,[25][26][27] and several others.…”

Section: Applicationmentioning

confidence: 99%

A Robust Iterative Approach for Solving Nonlinear Volterra Delay Integro–differential Equations

Ofem

Udofia

Igbokwe

2021

UMJ

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This paper presents a new iterative algorithm for approximating the fixed points of multivalued generalized $\alpha$–nonexpansive mappings. We study the stability result of our new iterative algorithm for a larger concept of stability known as weak $w^2$–stability. Weak and strong convergence results of the proposed iterative algorithm are also established. Furthermore, we show numerically that our new iterative algorithm outperforms several known iterative algorithms for multivalued generalized $\alpha$–nonexpansive mappings. Again, as an application, we use our proposed iterative algorithm to find the solution of nonlinear Volterra delay integro-differential equations. Finally, we provide an illustrative example to validate the mild conditions used in the result of the application part of this study. Our results improve, generalize and unify several results in the existing literature.

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“…Due to their importance, various methods have been imployed to approximate solutions of equilibrium and xed point problems (see, for example, [3,18,19,35,36] and the references contained therein). One of the common methods use is the proximal point method in which the convergence analysis has been considered when the bifunction g is monotone see [26].…”

Section: T Is Denoted Byf (T )mentioning

confidence: 99%

Inertial hybrid self-adaptive subgradient extragradient method for fixed point of quasi$-\phi-$nonexpansive multivalued mappings and equilibrium problem

Harbau¹

2021

Advances in the Theory of Nonlinear Analysis and Its Application

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In this paper, we propose a new inertial self-adaptive subgradient extragradient algorithm for approximating common solution in the set of pseudomonotone equilibrium problems and the set of xed point of nite family of quasi−φ−nonexpansive multivalued mappings in real uniformly convex Banach spaces and uniformly smooth Banach spaces. Strong convergence of the iterative scheme is established. Our results generalizes and improves several recent results annouced in the literature.

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A new fixed point algorithm for finding the solution of a delay differential equation

Cited by 23 publications

References 21 publications

New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem

A Robust Iterative Approach for Solving Nonlinear Volterra Delay Integro–differential Equations

Inertial hybrid self-adaptive subgradient extragradient method for fixed point of quasi$-\phi-$nonexpansive multivalued mappings and equilibrium problem

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