Pub Date : 2024-04-05DOI: 10.55630/serdica.2024.50.35-46
G. Singh, G. Singh
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.
{"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}
Pub Date : 2024-04-05DOI: 10.55630/serdica.2024.50.1-34
A. Corro, Carlos Riveros, José Carretero
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.
{"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}
Pub Date : 2024-01-04DOI: 10.55630/serdica.2023.49.283-300
Heramb Aiya, Yeshwant Valaulikar
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.
{"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}
Pub Date : 2024-01-04DOI: 10.55630/serdica.2023.49.269-282
I. Argyros, S. George
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.
{"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}
Pub Date : 2024-01-04DOI: 10.55630/serdica.2023.49.241-250
Gaurav Mittal, Rajendra Sharma
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.
{"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}
Pub Date : 2023-12-07DOI: 10.55630/serdica.2022.48.271-278
R. Divya, P. Chithra Devi
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}).
{"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}
Pub Date : 2023-12-07DOI: 10.55630/serdica.2022.48.279-296
G. Singh, G. Singh
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.
本文介绍了单位圆盘（E=left/{z/in/mathbb{C}:mid z mid<1/right/}）中关于对称点和共轭点的某些统一的近凸函数和准凸函数子类，并建立了这些类的前四个系数的上限。这项研究将激励该领域的其他研究人员研究更多类似的类。
{"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}
Pub Date : 2023-11-20DOI: 10.55630/serdica.2023.49.187-204
Mira Bivas, M. Krastanov, N. Ribarska
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.
{"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}
Pub Date : 2023-11-20DOI: 10.55630/serdica.2023.49.9-32
Alexander Ioffe
The paper is devoted to proving necessary optimality conditions for weak/intermediate/strong minimum of a generalized Bolza problem.
本文致力于证明广义博尔扎问题的弱/中/强最小值的必要最优条件。
{"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}
Pub Date : 2023-11-20DOI: 10.55630/serdica.2023.49.33-48
Tullio Zolezzi
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.
{"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}
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