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Study of a generalized subclass of meromorphic functions 研究广义的微变函数子类
Serdica Mathematical Journal Pub Date : 2024-04-05 DOI: 10.55630/serdica.2024.50.35-46
G. Singh, G. Singh
{"title":"Study of a generalized subclass of meromorphic functions","authors":"G. Singh, G. Singh","doi":"10.55630/serdica.2024.50.35-46","DOIUrl":"https://doi.org/10.55630/serdica.2024.50.35-46","url":null,"abstract":"This paper is concerned with a new subclass of meromorphic close-to-convex functions defined by means of subordination. various properties of this class such as coefficient estimates, inclusion relationship, distortion property and radius of meromorphic convexity, are established. Some earlier known results follow as special cases.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"7 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140736943","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 class of solutions of the n-dimensional generalized Helmholtz equation which describes generalized Weingarten hypersurfaces 描述广义魏格登超曲面的 n 维广义赫尔姆霍兹方程的一类解
Serdica Mathematical Journal Pub Date : 2024-04-05 DOI: 10.55630/serdica.2024.50.1-34
A. Corro, Carlos Riveros, José Carretero
{"title":"A class of solutions of the n-dimensional generalized Helmholtz equation which describes generalized Weingarten hypersurfaces","authors":"A. Corro, Carlos Riveros, José Carretero","doi":"10.55630/serdica.2024.50.1-34","DOIUrl":"https://doi.org/10.55630/serdica.2024.50.1-34","url":null,"abstract":"In this paper, we introduce the (n)-dimensional generalized Helmholtz equation and present explicit solutions to this equation in terms of biharmonic functions, in particular, we get solutions that depend on holomorphic functions. Also, we present explicit radial solutions for this equation and we provide explicit solutions to the (n)-dimensional Helmholtz equation. In addition, as an application we introduced two classes of generalized Weingarten hypersurfaces, namely, the RSHGW-hypersurfaces and the RSGW-hypersurfaces, associated with solutions of the (n)-dimensional generalized Helmholtz equation and classify the RSHGW-hypersurfaces of rotation. For (n=2), we obtain a Weierstrass type representation for these surfaces which depend of three holomorphic functions and we classify the RSHGW-surfaces and the RSGW-surfaces of rotation.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"19 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140739171","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: 1
Monotone iterative method for boundary value problem with linear condition of first order delay differential equation 带线性条件的一阶延迟微分方程边界值问题的单调迭代法
Serdica Mathematical Journal Pub Date : 2024-01-04 DOI: 10.55630/serdica.2023.49.283-300
Heramb Aiya, Yeshwant Valaulikar
{"title":"Monotone iterative method for boundary value problem with linear condition of first order delay differential equation","authors":"Heramb Aiya, Yeshwant Valaulikar","doi":"10.55630/serdica.2023.49.283-300","DOIUrl":"https://doi.org/10.55630/serdica.2023.49.283-300","url":null,"abstract":"In this paper we discuss the boundary value problem for a first order delay differential equation of the type, (y'(t) + lambda y(t) = f(t, y(t - r))). We prove the existence of solution between weakly coupled lower and upper solution by assuming (f) to be a non-decreasing function in the second coordinate. Further, we use this existence result to establish monotone iterative method, where we obtain increasing as well as decreasing sequence of functions whose limits are a solution of the boundary value problem. The sequence of functions obtained are solutions of some defined boundary value problem with linear condition of linear delay differential equation.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"49 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139385832","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
Newton's method for generalized equations under weak conditions 弱条件下广义方程的牛顿法
Serdica Mathematical Journal Pub Date : 2024-01-04 DOI: 10.55630/serdica.2023.49.269-282
I. Argyros, S. George
{"title":"Newton's method for generalized equations under weak conditions","authors":"I. Argyros, S. George","doi":"10.55630/serdica.2023.49.269-282","DOIUrl":"https://doi.org/10.55630/serdica.2023.49.269-282","url":null,"abstract":"A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"29 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139384426","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 short note on the Wedderburn components of a semisimple finite group algebra 半简单有限群代数的韦德本分量简述
Serdica Mathematical Journal Pub Date : 2024-01-04 DOI: 10.55630/serdica.2023.49.241-250
Gaurav Mittal, Rajendra Sharma
{"title":"A short note on the Wedderburn components of a semisimple finite group algebra","authors":"Gaurav Mittal, Rajendra Sharma","doi":"10.55630/serdica.2023.49.241-250","DOIUrl":"https://doi.org/10.55630/serdica.2023.49.241-250","url":null,"abstract":"One of the classical problems in the subject of group algebras is that of deducing Wedderburn decomposition of a finite semisimple group algebra. In this short note, we discuss how to check whether a matrix ring over a finite field is a Wedderburn component of the Wedderburn decomposition of a group algebra or not. Finally, we formulate an open problem in this direction.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"64 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139386865","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
Harmonious colouring of line graph of commuting and non-commuting graph of D_{2n} D_{2n} 交换图和非交换图的线图的和谐着色
Serdica Mathematical Journal Pub Date : 2023-12-07 DOI: 10.55630/serdica.2022.48.271-278
R. Divya, P. Chithra Devi
{"title":"Harmonious colouring of line graph of commuting and non-commuting graph of D_{2n}","authors":"R. Divya, P. Chithra Devi","doi":"10.55630/serdica.2022.48.271-278","DOIUrl":"https://doi.org/10.55630/serdica.2022.48.271-278","url":null,"abstract":"Harmonious coloring of graph (G) is a proper vertex coloring, where each pair of colors occurs at most on one pair of adjacent vertices. Minimum number of colors required for Harmonious coloring of (G) is the harmonious chromatic number, (chi_{H}(G)). Here we determine the Harmonious chromatic number of the line graph of commuting graph and non-commuting graph of the dihedral group, (D_{2n}).","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139185563","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
Coefficient estimates for some generalized subclasses of analytic functions with respect to symmetric and conjugate points 关于对称点和共轭点的某些广义解析函数子类的系数估计
Serdica Mathematical Journal Pub Date : 2023-12-07 DOI: 10.55630/serdica.2022.48.279-296
G. Singh, G. Singh
{"title":"Coefficient estimates for some generalized subclasses of analytic functions with respect to symmetric and conjugate points","authors":"G. Singh, G. Singh","doi":"10.55630/serdica.2022.48.279-296","DOIUrl":"https://doi.org/10.55630/serdica.2022.48.279-296","url":null,"abstract":"In this paper, we introduce certain unified subclasses of close-to-convex functions and quasi-convex functions with respect to symmetric and conjugate points in the unit disc (E=left{zinmathbb{C}:mid z mid<1right}) and establish the upper bounds of the first four coefficients for these classes. This study will work as a motivation for the other researchers in this field to study some more similar classes.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"9 3-4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139185704","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
Linearization of differential inclusions 微分夹杂的线性化
Serdica Mathematical Journal Pub Date : 2023-11-20 DOI: 10.55630/serdica.2023.49.187-204
Mira Bivas, M. Krastanov, N. Ribarska
{"title":"Linearization of differential inclusions","authors":"Mira Bivas, M. Krastanov, N. Ribarska","doi":"10.55630/serdica.2023.49.187-204","DOIUrl":"https://doi.org/10.55630/serdica.2023.49.187-204","url":null,"abstract":"In this paper we extend the approach of Dubovickiĭ and Miljutin for linearization of the dynamics of smooth control systems to a non-smooth setting. We consider dynamics governed by a differential inclusion and we study the Clarke tangent cone to the set of all admissible trajectories starting from a fixed point. Our approach is based on the classical Filippov’s theorem and on the important property “subtransversality” of two closed sets.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139256138","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 necessary conditions in the generalized Bolza problem 论广义波尔扎问题中的必要条件
Serdica Mathematical Journal Pub Date : 2023-11-20 DOI: 10.55630/serdica.2023.49.9-32
Alexander Ioffe
{"title":"On necessary conditions in the generalized Bolza problem","authors":"Alexander Ioffe","doi":"10.55630/serdica.2023.49.9-32","DOIUrl":"https://doi.org/10.55630/serdica.2023.49.9-32","url":null,"abstract":"The paper is devoted to proving necessary optimality conditions for weak/intermediate/strong minimum of a generalized Bolza problem.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139259727","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
An upper bound for a condition number theorem of variational inequalities 变分不等式条件数定理的上界
Serdica Mathematical Journal Pub Date : 2023-11-20 DOI: 10.55630/serdica.2023.49.33-48
Tullio Zolezzi
{"title":"An upper bound for a condition number theorem of variational inequalities","authors":"Tullio Zolezzi","doi":"10.55630/serdica.2023.49.33-48","DOIUrl":"https://doi.org/10.55630/serdica.2023.49.33-48","url":null,"abstract":"Nonlinear variational inequalities in Banach spaces are considered. A notion of (absolute) condition number with respect to the right-hand side is introduced. A distance among variational inequalities is defined. We prove that the distance to suitably restricted ill-conditioned variational inequalities is bounded from above by a multiple of the reciprocal of the condition number. By using an analogous lower bound of the companion paper [14], we obtain a full condition number theorem for variational inequalities. The particular case of convex optimization problems is also considered. Known results dealing with optimization problems are thereby generalized.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"192 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139255848","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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