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Conjugated Gradient with Four Terms for Nonlinear Unconstrained Optimization 非线性无约束优化的四项共轭梯度
General Letters in Mathematics Pub Date : 2022-03-01 DOI: 10.31559/glm2022.12.1.5
A. Mustafa
{"title":"Conjugated Gradient with Four Terms for Nonlinear Unconstrained Optimization","authors":"A. Mustafa","doi":"10.31559/glm2022.12.1.5","DOIUrl":"https://doi.org/10.31559/glm2022.12.1.5","url":null,"abstract":"The nonlinear conjugate gradient (GJG) technique is an effective tool for addressing minimization on a huge scale. It can be used in a variety of applications., We presented a novel conjugate gradient approach based on two hypotheses, and we equalized the two hypotheses and retrieved the good parameter in this article. To get a new conjugated gradient, we multiplied the new parameter by a control parameter and substituted it in the second equation. a fresh equation for 𝛽𝑘 is proposed. It has global convergence qualities. When compared to the two most common conjugate gradient techniques, our algorithm outperforms them in terms of both the number of iterations (NOIS) and the number of functions (NOFS). The new technique is efficient in real computing and superior to previous comparable approaches in many instances, according to numerical results.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45931925","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}
引用次数: 0
Taylor approximation for solving linear and nonlinear Ill-Posed Volterra equations via an iteration method 迭代法求解线性和非线性病态Volterra方程的Taylor近似
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.31559/glm2021.11.2.1
Somia Guechi, Moufida Guechi
{"title":"Taylor approximation for solving linear and nonlinear Ill-Posed Volterra equations via an iteration method","authors":"Somia Guechi, Moufida Guechi","doi":"10.31559/glm2021.11.2.1","DOIUrl":"https://doi.org/10.31559/glm2021.11.2.1","url":null,"abstract":"In this paper, we present two algorithms for the approximate or exact solution of a class of Volterra integral equations of first kind. As well known, this is an ill posed problem, but we convert it to well-posedness of the second kind Volterra problems, then we apply the variational iteration method. Finally, we present two examples which show the performance and effciency of our method.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45954842","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}
引用次数: 2
On A Certain Subclass Of Analytic Functions Defined By Linear Operator 关于由线性算子定义的解析函数的一个子类
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0014
B. Venkateswarlu, P. Reddy, Santosh M. Popade, R. N. Ingle
{"title":"On A Certain Subclass Of Analytic Functions Defined By Linear Operator","authors":"B. Venkateswarlu, P. Reddy, Santosh M. Popade, R. N. Ingle","doi":"10.2478/gm-2021-0014","DOIUrl":"https://doi.org/10.2478/gm-2021-0014","url":null,"abstract":"Abstract In this paper, we introduce and study a new class k − ŨSs(a, c, µ, γ, t) of analytic functions in the open unit disc U with negative coefficients and obtain coefficient estimates, neighborhoods and partial sums for functions f belonging to this class.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"37 1","pages":"57 - 68"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74701600","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}
引用次数: 0
Bohr Radius for Goodman-Ronning Type Harmonic Univalent Functions Goodman-Ronning型调和一元函数的玻尔半径
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0018
S. Varma, T. Rosy
{"title":"Bohr Radius for Goodman-Ronning Type Harmonic Univalent Functions","authors":"S. Varma, T. Rosy","doi":"10.2478/gm-2021-0018","DOIUrl":"https://doi.org/10.2478/gm-2021-0018","url":null,"abstract":"Abstract In this paper we obtain the sharp Bohr radius, Bohr-Rogosinski radius, improved Bohr-radius and refined Bohr radius for the functions in the class GH¯0(γ) G_{bar H}^0left( gamma right) of Goodman-Ronning type harmonic univalent functions with negative coeffcients.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"78 1","pages":"107 - 126"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74020676","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}
引用次数: 0
Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship 随机约束下单函数指标建模中一种非参数条件分位数估计的渐近结果
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0020
Nadia Kadiri, A. Rabhi, Fatima Akkal
{"title":"Asymptotic Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship","authors":"Nadia Kadiri, A. Rabhi, Fatima Akkal","doi":"10.2478/gm-2021-0020","DOIUrl":"https://doi.org/10.2478/gm-2021-0020","url":null,"abstract":"Abstract The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"39 1","pages":"137 - 168"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84670062","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}
引用次数: 0
(p, q)–derivative on univalent functions associated with subordination structure 具有从属结构的一元函数的(p, q) -导数
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0017
S. Najafzadeh
{"title":"(p, q)–derivative on univalent functions associated with subordination structure","authors":"S. Najafzadeh","doi":"10.2478/gm-2021-0017","DOIUrl":"https://doi.org/10.2478/gm-2021-0017","url":null,"abstract":"Abstract By means of Jackson’s (p, q)–derivative a new class of univalent functions based on subordination is defined. We evoke some geometric properties such as coefficient estimate, convolution preserving, convexity and radii properties of this class of functions are obtained.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"3 1","pages":"99 - 106"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79973538","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}
引用次数: 0
A New Coefficient of Conjugate Gradient Method with Global Convergence for Unconstrained Optimization Problems 无约束优化问题的一种新的全局收敛共轭梯度系数法
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.31559/glm2021.11.2.3
Mardeen Sh. Taher, S. Shareef
{"title":"A New Coefficient of Conjugate Gradient Method with Global Convergence for Unconstrained Optimization Problems","authors":"Mardeen Sh. Taher, S. Shareef","doi":"10.31559/glm2021.11.2.3","DOIUrl":"https://doi.org/10.31559/glm2021.11.2.3","url":null,"abstract":"In this article, we defined a new coefficient formula of the conjugate gradient method for solving non linear unconstrained optimization problems. The new formula β new k is type of line search and the idea of our work is to focus on modification the Perry’s suggestion. We further show that global convergence result of new formula is recognized under Wolf-Powell line search. It is shown that the new CG coefficient satisfied sufficient descent conditions. In the end, numerical experiments with the collection of test functions show that the new β new k is more effective compared to some other standard formulas such as β H−S k , β Perry k and β D−Y k .","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42545415","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}
引用次数: 0
On Certain Subclass of Starlike Functions with Negative Coefficients Associated with Erdelyi-Kober Integral Operator 关于与Erdelyi-Kober积分算子相关的负系数星形函数的某些子类
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0015
S. Prathiba, T. Rosy
{"title":"On Certain Subclass of Starlike Functions with Negative Coefficients Associated with Erdelyi-Kober Integral Operator","authors":"S. Prathiba, T. Rosy","doi":"10.2478/gm-2021-0015","DOIUrl":"https://doi.org/10.2478/gm-2021-0015","url":null,"abstract":"Abstract In this research article, making use of Erdelyi-Kober integral operator, we define a new subclass Ta,cµ(α, β, γ, A, B) of starlike functions with negative coefficient. Various properties like coefficient estimates, neighbourhood results, integral means, partial sums and subordination results are examined for this class.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"30 1","pages":"69 - 82"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82382633","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}
引用次数: 0
The Fekete-Szego Theorem for Close-to-convex Functions Associated with The Koebe Type Function 与Koebe型函数相关的近凸函数的Fekete-Szego定理
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0019
S. Rathi, S. C. Soh
{"title":"The Fekete-Szego Theorem for Close-to-convex Functions Associated with The Koebe Type Function","authors":"S. Rathi, S. C. Soh","doi":"10.2478/gm-2021-0019","DOIUrl":"https://doi.org/10.2478/gm-2021-0019","url":null,"abstract":"Abstract This paper deals with the class S containing functions which are analytic and univalent in the open unit disc U = {z ∈ ℂ : |z| < 1}. Functions f in S are normalized by f(0) = 0 and f′(0) = 1 and has the Taylor series expansion of the form f(z)=z+∑n=2∞anzn fleft( z right) = z + sumlimits_{n = 2}^infty {{a_n}{z^n}} . In this paper we investigate on the subclass of S of close-to-convex functions denoted as Cgα(λ, δ) where function f ∈ Cgα(λ, δ) satisfies Re{ eiλzf′(z)gα(z) } {mathop{rm Re}nolimits} left{ {{e^{ilambda }}{{zf'left( z right)} over {galpha left( z right)}}} right} for | λ | δ, 0 ≤ δ < 1, 0 ≤ α ≤ 1 and gα=z(1−αz)2 {g_alpha } = {z over {{{left( {1 - alpha z} right)}^2}}} . The aim of the present paper is to find the upper bound of the Fekete-Szego functional |a3 − µa22| for the class Cgα(λ, δ). The results obtained in this paper is significant in the sense that it can be used in future research in this field, particularly in solving coefficient inequalities such as the Hankel determinant problems and also the Fekete-Szego problems for other subclasses of univalent functions.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"34 7 1","pages":"127 - 136"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82787936","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}
引用次数: 0
Approximating intuitionistic fuzzy fractals by densifiability techniques 用密度技术逼近直觉模糊分形
General Letters in Mathematics Pub Date : 2021-12-01 DOI: 10.2478/gm-2021-0011
G. García
{"title":"Approximating intuitionistic fuzzy fractals by densifiability techniques","authors":"G. García","doi":"10.2478/gm-2021-0011","DOIUrl":"https://doi.org/10.2478/gm-2021-0011","url":null,"abstract":"Abstract We present a sequence of sets converging, under suitable conditions and respect to the Hausdorff intuitionistic fuzzy metric, to the attractor set of certain intuitionistic fuzzy iterated function systems. For this goal, we will introduce a fuzzy version of the so called α-dense curves which have been used by the author to approximate, with arbitrarily small and controlled error, the attractor set of certain (metric) iterated function systems. In this way, we relate the above mentioned concepts of the intuitionistic fuzzy metric spaces with the α-density theory.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"11 1","pages":"3 - 21"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89296693","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}
引用次数: 0
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