Over the past decade, exponential Diophantine equations of the form ax + by = wn have been studied as if they were a phenomenon. In particular, numerous articles have focused on the cases where n = 2 or n = 4 and 2 ≤ a, b ≤ 200. However, these articles are primarily concerned with determining whether the left-hand side of the equation needs to consist of more than twoexponentials. Therefore, in this article, we investigate the exponential Diophantine equation in the form ax + by + cz = w2, using only elementary tools related to modulo concepts. We present three theorems in which the variables a, b and c vary under certain conditions, and three additional theorems where the variable c is fixed at 7. Furthermore, if we restrict our parameters a, b and cto 2 ≤ a ≤ b ≤ c ≤ 20, then 1,330 equations have been considered. Our results confirm that 135 of these equations have been fully clarified.
在过去的十年里，人们研究了ax + by = wn形式的指数丢番图方程，好像它们是一种现象。特别是，许多文章都关注于n = 2或n = 4且2≤a, b≤200的情况。然而，这些文章主要关注的是确定方程的左边是否需要由两个以上的指数组成。因此，在本文中，我们只使用与模概念相关的基本工具，研究ax + by + cz = w2形式的指数丢芬图方程。我们给出了变量a, b和c在一定条件下变化的三个定理，以及变量c固定为7的另外三个定理。进一步，如果我们将参数a、b和c限制为2≤a≤b≤c≤20，则考虑了1330个方程。我们的结果证实，其中135个方程已经完全澄清。
{"title":"On the Diophantine Equations $a^x+b^y+c^z=w^2$","authors":"Kittipong Laipaporn, Saowapak Kaewchay, Adisak Karnbanjong","doi":"10.29020/nybg.ejpam.v16i4.4936","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4936","url":null,"abstract":"Over the past decade, exponential Diophantine equations of the form ax + by = wn have been studied as if they were a phenomenon. In particular, numerous articles have focused on the cases where n = 2 or n = 4 and 2 ≤ a, b ≤ 200. However, these articles are primarily concerned with determining whether the left-hand side of the equation needs to consist of more than twoexponentials. Therefore, in this article, we investigate the exponential Diophantine equation in the form ax + by + cz = w2, using only elementary tools related to modulo concepts. We present three theorems in which the variables a, b and c vary under certain conditions, and three additional theorems where the variable c is fixed at 7. Furthermore, if we restrict our parameters a, b and cto 2 ≤ a ≤ b ≤ c ≤ 20, then 1,330 equations have been considered. Our results confirm that 135 of these equations have been fully clarified.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4945
Alanoud Almutairi
This paper presents a study on the oscillatory behavior of solutions to even-order neutral differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first-order delay differential equations, Riccati technique and integral averages technique. The results of this work contribute to a deeper understanding of even-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area.
{"title":"Oscillatory Properties Test for Even-Order Di§erential Equations of Neutral type","authors":"Alanoud Almutairi","doi":"10.29020/nybg.ejpam.v16i4.4945","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4945","url":null,"abstract":"This paper presents a study on the oscillatory behavior of solutions to even-order neutral differential equations involving p-Laplacian-like operator. We obtain oscillation criteria using techniques from first-order delay differential equations, Riccati technique and integral averages technique. The results of this work contribute to a deeper understanding of even-order differential equations and their connections to various branches of mathematics and practical sciences. The findings emphasize the importance of continued research in this area.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4930
Ali Kandil, Y. S. Hamed
This work deals with modeling and controlling the oscillations of a horizontally-supported car under the effect of a nonlinear spring, a damper, and a harmonic excitation external force. The proposed controller is the integral resonant controller (IRC) which is a first order oscillator coupled the car via a linear variable differential transformer (LVDT) and a servo-controlled linear actuator(SCLA). The multiple scales perturbation method is used to obtain an approximate solution and stability analyses are carried out. Based on the stability analysis, the optimum values of the controller parameters are recommended in this work for a better control operation. Several response curves are plotted for clarifying the concept of the proposed integral resonant control algorithm.A numerical simulation of the car’s motion is achieved by numerically integrating the model equations with the 4th order Rung-Kutta algorithm. The applied controller can treat the severe jumps in the oscillation amplitude where it is suppressed at different conditions of forward and backward sweeping of the amplitude and frequency of the external excitation force.
{"title":"Integral Resonant Controller for Suppressing Car’s Oscillations and Eliminating its Inherent Jump Phenomenon","authors":"Ali Kandil, Y. S. Hamed","doi":"10.29020/nybg.ejpam.v16i4.4930","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4930","url":null,"abstract":"This work deals with modeling and controlling the oscillations of a horizontally-supported car under the effect of a nonlinear spring, a damper, and a harmonic excitation external force. The proposed controller is the integral resonant controller (IRC) which is a first order oscillator coupled the car via a linear variable differential transformer (LVDT) and a servo-controlled linear actuator(SCLA). The multiple scales perturbation method is used to obtain an approximate solution and stability analyses are carried out. Based on the stability analysis, the optimum values of the controller parameters are recommended in this work for a better control operation. Several response curves are plotted for clarifying the concept of the proposed integral resonant control algorithm.A numerical simulation of the car’s motion is achieved by numerically integrating the model equations with the 4th order Rung-Kutta algorithm. The applied controller can treat the severe jumps in the oscillation amplitude where it is suppressed at different conditions of forward and backward sweeping of the amplitude and frequency of the external excitation force.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4922
Cordy Jourvel Itoua-Tsele, Antoine Filankembo Ouassissou
Groundwater plays an important role in feeding many families and societies whose access to water is a huge problem for several reasons, then the mathematical model is an essential part of a hydrologist’s daily life to understand the physical phenomena. In this paper, we used Dupuit’s assumption to reduce the groundwater flow equation and integrated vertically it to obtainthe diffusivity equation in terms of the hydraulic head, further, the introduction of fundamental ideas in groundwater research, including vocabulary and mathematics will give readers the basis knowledge. Numerous numerical techniques can be recognized, the unstructured finite volume method was used to solve a transient diffusivity equation through a coastal confined aquifer. Theconstructed finite volume schemes are used to study the distribution of hydraulic heads in the model domain, to determine water table fluctuations, and to predict the drawdown phenomena.
{"title":"Analytical Solution of Vertically Integrated Equations of a Confined Aquifer in two-dimension using Finite Volume method","authors":"Cordy Jourvel Itoua-Tsele, Antoine Filankembo Ouassissou","doi":"10.29020/nybg.ejpam.v16i4.4922","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4922","url":null,"abstract":"Groundwater plays an important role in feeding many families and societies whose access to water is a huge problem for several reasons, then the mathematical model is an essential part of a hydrologist’s daily life to understand the physical phenomena. In this paper, we used Dupuit’s assumption to reduce the groundwater flow equation and integrated vertically it to obtainthe diffusivity equation in terms of the hydraulic head, further, the introduction of fundamental ideas in groundwater research, including vocabulary and mathematics will give readers the basis knowledge. Numerous numerical techniques can be recognized, the unstructured finite volume method was used to solve a transient diffusivity equation through a coastal confined aquifer. Theconstructed finite volume schemes are used to study the distribution of hydraulic heads in the model domain, to determine water table fluctuations, and to predict the drawdown phenomena.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4734
Chawalit Boonpok, Jeeranunt Khampakdee
This paper is concerned with the concepts of upper and lower weakly sβ(⋆)-continuous multifunctions. Moreover, some characterizations of upper and lower weakly sβ(⋆)-continuous multifunctions are investigated.
{"title":"Upper and Lower weak $sbeta(star)$-continuity","authors":"Chawalit Boonpok, Jeeranunt Khampakdee","doi":"10.29020/nybg.ejpam.v16i4.4734","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4734","url":null,"abstract":"This paper is concerned with the concepts of upper and lower weakly sβ(⋆)-continuous multifunctions. Moreover, some characterizations of upper and lower weakly sβ(⋆)-continuous multifunctions are investigated.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4877
Javier Hassan, Sergio R. Canoy, Jr.
Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy total hop domination number of a graph G is between the total hop domination number and twice the Grundy hop domination number of G. Moreover, determine values or bounds of the Grundy total hop domination number of some graphs.
{"title":"Grundy Total Hop Dominating Sequences in Graphs","authors":"Javier Hassan, Sergio R. Canoy, Jr.","doi":"10.29020/nybg.ejpam.v16i4.4877","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4877","url":null,"abstract":"Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy total hop domination number of a graph G is between the total hop domination number and twice the Grundy hop domination number of G. Moreover, determine values or bounds of the Grundy total hop domination number of some graphs.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4901
Mary Joy R. Latayada
Let $N_m$ be the set of positive integers $1, 2, cdots, m$ and $S subseteq N_m$. In 2000, J. Caumeran and R. Corcino made a thorough investigation on counting restricted functions $f_{|S}$ under each of the following conditions:begin{itemize}item[(textit{a})]$f(a) leq a$, $forall a in S$;item[(textit{b})] $f(a) leq g(a)$, $forall a in S$ where $g$ is any nonnegative real-valued continuous functions;item[(textit{c})] $g_1(a) leq f(a) leq g_2(a)$, $forall a in S$, where $g_1$ and $g_2$ are any nonnegative real-valued continuous functions.end{itemize}Several formulae and identities were also obtained by Caumeran using basic concepts in combinatorics.In this paper, we count those restricted functions under condition $f(a) leq a$, $forall a in S$, which is one-to-one and onto, and establish some formulas and identities parallel to those obtained by J. Caumeran and R. Corcino.
设$N_m$为正整数$1, 2, cdots, m$和$S subseteq N_m$的集合。2000年，J. Caumeran和R. Corcino在以下条件下对计数限制函数$f_{|S}$进行了深入的研究:begin{itemize}item[(textit{a})]$f(a) leq a$， $forall a in S$;item[(textit{b})] $f(a) leq g(a)$， $forall a in S$其中$g$为任意非负实值连续函数;item[(textit{c})] $g_1(a) leq f(a) leq g_2(a)$， $forall a in S$，其中$g_1$和$g_2$为任意非负实值连续函数。end{itemize}利用组合学的基本概念，用柯曼方法得到了几个公式和恒等式。在$f(a) leq a$, $forall a in S$条件下，我们计算了这些限制函数，它们是一对一和映上的，并建立了一些与J. Caumeran和R. Corcino的公式和恒等式平行的公式和恒等式。
{"title":"On the Number of Restricted One-to-One and Onto Functons Having Integral Coordinates","authors":"Mary Joy R. Latayada","doi":"10.29020/nybg.ejpam.v16i4.4901","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4901","url":null,"abstract":"Let $N_m$ be the set of positive integers $1, 2, cdots, m$ and $S subseteq N_m$. In 2000, J. Caumeran and R. Corcino made a thorough investigation on counting restricted functions $f_{|S}$ under each of the following conditions:begin{itemize}item[(textit{a})]$f(a) leq a$, $forall a in S$;item[(textit{b})] $f(a) leq g(a)$, $forall a in S$ where $g$ is any nonnegative real-valued continuous functions;item[(textit{c})] $g_1(a) leq f(a) leq g_2(a)$, $forall a in S$, where $g_1$ and $g_2$ are any nonnegative real-valued continuous functions.end{itemize}Several formulae and identities were also obtained by Caumeran using basic concepts in combinatorics.In this paper, we count those restricted functions under condition $f(a) leq a$, $forall a in S$, which is one-to-one and onto, and establish some formulas and identities parallel to those obtained by J. Caumeran and R. Corcino.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4931
Jules Ouya, Arouna Ouedraogo
In this work, we show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosity density-dependent for large initial data. With a pressure law of the form ρ2, we represent the vertical velocity as a function of the density and the horizontal one which will be important in using Faedo-Galerkin method to obtain the global existence of the approximate solutions. In analogy with the cases in [28] and [26, 27], we prove that the weak solutions satisfy the basic energy inequality and the Bresch-Desjardins entropy inequality. Based on these estimates and using compactness arguments, we prove the global existence of weak solutions of (1.1) by vanishing the parameters in our approximate system step by step.
{"title":"Global Existence of Weak Solutions to 3D Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosity","authors":"Jules Ouya, Arouna Ouedraogo","doi":"10.29020/nybg.ejpam.v16i4.4931","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4931","url":null,"abstract":"In this work, we show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosity density-dependent for large initial data. With a pressure law of the form ρ2, we represent the vertical velocity as a function of the density and the horizontal one which will be important in using Faedo-Galerkin method to obtain the global existence of the approximate solutions. In analogy with the cases in [28] and [26, 27], we prove that the weak solutions satisfy the basic energy inequality and the Bresch-Desjardins entropy inequality. Based on these estimates and using compactness arguments, we prove the global existence of weak solutions of (1.1) by vanishing the parameters in our approximate system step by step.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4928
Iman ALdarawi, Banan Maayah, Eman Aldabbas, Eman Abuteen
This paper explores the solutions of certain fractional partial differential equations using two methods; the first method involves separation of variables, which is a common technique for solving partial differential equations. However, since many equations cannot be separated in this way, the tensor product of Banach spaces method is applied to find the atomic solutions. To solve the resulting ordinary differential equations, the reproducing Kernel Hilbert space method is used to find numerical solutions, which are then used to find the numerical solution of the partial differential equation. The residual errors indicate that this method is effective and powerful. In summary, this paper presents a study on the solutions of certain fractional partial differential equations using two methods and demonstrates the effectiveness of these methods in finding numerical solutions.
{"title":"Numerical Solutions of Some Classes of Partial Differential Equations of Fractional Order","authors":"Iman ALdarawi, Banan Maayah, Eman Aldabbas, Eman Abuteen","doi":"10.29020/nybg.ejpam.v16i4.4928","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4928","url":null,"abstract":"This paper explores the solutions of certain fractional partial differential equations using two methods; the first method involves separation of variables, which is a common technique for solving partial differential equations. However, since many equations cannot be separated in this way, the tensor product of Banach spaces method is applied to find the atomic solutions. To solve the resulting ordinary differential equations, the reproducing Kernel Hilbert space method is used to find numerical solutions, which are then used to find the numerical solution of the partial differential equation. The residual errors indicate that this method is effective and powerful. In summary, this paper presents a study on the solutions of certain fractional partial differential equations using two methods and demonstrates the effectiveness of these methods in finding numerical solutions.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-30DOI: 10.29020/nybg.ejpam.v16i4.4949
Ali Zein
A family of fifth-order iterative methods is proposed for solving nonlinear equations using the weight function technique. This family offers flexibility through its structure and the choice of weight functions, resulting in a wide range of new specific schemes. It is demonstrated that this proposed family includes several well-known and recent methods as special cases. In addition, several new particular methods are designed to achieve better results than existing methods of the same type. Convergence analysis is conducted, and numerical examples in both real and complex domains are provided for several specific schemes within the proposed family. Comparisons between the existing methods within this family and the newly introduced methods generally indicate improved performance among the new members. Notably, the study of complex dynamics and basins of attraction reveals that our new specific schemes have broader sets of initial points that lead to convergence.
{"title":"A General Family of Fifth-order Iterative Methods for Solving Nonlinear Equations","authors":"Ali Zein","doi":"10.29020/nybg.ejpam.v16i4.4949","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i4.4949","url":null,"abstract":"A family of fifth-order iterative methods is proposed for solving nonlinear equations using the weight function technique. This family offers flexibility through its structure and the choice of weight functions, resulting in a wide range of new specific schemes. It is demonstrated that this proposed family includes several well-known and recent methods as special cases. In addition, several new particular methods are designed to achieve better results than existing methods of the same type. Convergence analysis is conducted, and numerical examples in both real and complex domains are provided for several specific schemes within the proposed family. Comparisons between the existing methods within this family and the newly introduced methods generally indicate improved performance among the new members. Notably, the study of complex dynamics and basins of attraction reveals that our new specific schemes have broader sets of initial points that lead to convergence.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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