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.
{"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}
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.
{"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}
B. Venkateswarlu, P. Reddy, Santosh M. Popade, R. N. Ingle
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.
{"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}
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.
{"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}
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.
{"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}
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.
{"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}
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 .
本文定义了求解非线性无约束优化问题的共轭梯度法的一个新的系数公式。新公式β新k是直线搜索的类型，我们的工作重点是修改佩里的建议。进一步证明了在Wolf-Powell线搜索下，新公式的全局收敛结果是可识别的。结果表明，新的CG系数满足下降的充分条件。最后，用测试函数集合进行了数值实验，结果表明，与β H−S k、β Perry k和β D−Y k等标准公式相比，new β new k更为有效。
{"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}
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.
摘要本文利用Erdelyi-Kober积分算子，定义了具有负系数的星形函数的新子类Ta,cµ(α， β， γ， a, B)。各种性质，如系数估计，邻域结果，积分均值，部分和和从属的结果检查了这类。
{"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}
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.
摘要研究了开单位圆盘U = {z∈:|z| < 1}上含有一元解析函数的S类。S中的函数f归一化为f(0) = 0和f '(0) = 1，其泰勒级数展开式为f(z)=z+∑n=2∞和zn f left (z right)=z+ sumlimits ＿n =2{ ^ }infty a＿nz{{^n}{。本文研究了近似凸函数S的子类Cgα(λ， δ)，其中函数f∈Cgα(λ， δ)满足Re - λzf ' (z)}}gα(z) {}{mathop{rm Re}nolimits}left ｛{{e^{i lambda zf'}}{{left (z right) }over g{alphaleft (z right) }}}right｝对于| λ | δ， 0≤δ < 1，0≤α≤1,gα=z(1−αz)2 {g＿alpha =}z {over{{{left ({1 -alpha z }right)}^2}}}。本文的目的是求一类Cgα(λ， δ)的Fekete-Szego泛函|a3−µa22|的上界。本文得到的结果具有重要意义，可以用于该领域的未来研究，特别是在求解系数不等式如Hankel行列式问题和其他一元函数子类的Fekete-Szego问题方面。
{"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}
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.
{"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}
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