Rajendra Prasad, Abhinav Verma, Vindhyachal Singh Yadav, Abdul Haseeb, Mohd Bilal
For an $LP$-Kenmotsu manifold of dimension $m$ (briefly, ${(LPK)_{m}}$) admitting Bach almost solitons $(g,zeta,lambda)$, we have explored the characteristics of norm of Ricci operator. Besides, we have studied the Bach tensor on Lorentzian para-Kenmotsu manifolds to have an $eta$-Einstein manifold. Afterwards, we have proved that Bach almost solitons $(g,zeta,lambda)$ are always steady when, a Lorentzian para-Kenmotsu manifold of dimension-three has Bach almost solitons.
{"title":"LP-Kenmotsu manifolds admitting Bach almost solitons","authors":"Rajendra Prasad, Abhinav Verma, Vindhyachal Singh Yadav, Abdul Haseeb, Mohd Bilal","doi":"10.32323/ujma.1443527","DOIUrl":"https://doi.org/10.32323/ujma.1443527","url":null,"abstract":"For an $LP$-Kenmotsu manifold of dimension $m$ (briefly, ${(LPK)_{m}}$) admitting Bach almost solitons $(g,zeta,lambda)$, we have explored the characteristics of norm of Ricci operator. Besides, we have studied the Bach tensor on Lorentzian para-Kenmotsu manifolds to have an $eta$-Einstein manifold. Afterwards, we have proved that Bach almost solitons $(g,zeta,lambda)$ are always steady when, a Lorentzian para-Kenmotsu manifold of dimension-three has Bach almost solitons.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":" 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141128785","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}
This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples.
本文讨论了从 Caputo 意义上考虑的线性分数 Fredholm-Volterra 微分方程 (IDE)。为此，本文使用 Laguerre 多项式构建了一种近似方法，以获得线性分数 Fredholm-Volterra IDE 的解。通过这种近似方法，利用适当的定位点将 IDE 转化为线性代数方程系统。此外，还首次在文献中为 Laguerre 多项式的 Caputo 分数导数建立了一个新颖而精确的矩阵表达式和相关的显式矩阵表述。此外，通过在大量实例中实施该方法，对所提出方法的结果与文献中方法的结果进行了比较。
{"title":"Laguerre collocation approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations","authors":"Dilek Varol, Ayşegül Daşcıoğlu","doi":"10.32323/ujma.1390222","DOIUrl":"https://doi.org/10.32323/ujma.1390222","url":null,"abstract":"This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"2 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139859564","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}
This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples.
本文讨论了从 Caputo 意义上考虑的线性分数 Fredholm-Volterra 微分方程 (IDE)。为此，本文使用 Laguerre 多项式构建了一种近似方法，以获得线性分数 Fredholm-Volterra IDE 的解。通过这种近似方法，利用适当的定位点将 IDE 转化为线性代数方程系统。此外，还首次在文献中为 Laguerre 多项式的 Caputo 分数导数建立了一个新颖而精确的矩阵表达式和相关的显式矩阵表述。此外，通过在大量实例中实施该方法，对所提出方法的结果与文献中方法的结果进行了比较。
{"title":"Laguerre collocation approach of Caputo Fractional Fredholm-Volterra Integro-Differential Equations","authors":"Dilek Varol, Ayşegül Daşcıoğlu","doi":"10.32323/ujma.1390222","DOIUrl":"https://doi.org/10.32323/ujma.1390222","url":null,"abstract":"This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"272 1‐4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139799387","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}
This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, H"{o}lder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples.
{"title":"New Perspectives on Fractional Milne-Type Inequalities: Insights from Twice-Differentiable Functions","authors":"Henok Desalegn Desta, H. Budak, Hasan Kara","doi":"10.32323/ujma.1397051","DOIUrl":"https://doi.org/10.32323/ujma.1397051","url":null,"abstract":"This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, H\"{o}lder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":" 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139618913","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}
This paper introduces the definition of Fermatean fuzzy soft sets and some of its properties. The Fermatean fuzzy soft sets are a parameterized family of Fermatean fuzzy soft sets. Fermatean fuzzy soft sets are a generalization of soft sets. Remarkably, the basic properties and operations of Fermatean soft sets are given. Entropy and distance measures are defined for the Fermatean fuzzy soft sets. Further, we propose two algorithms for the decision-making problem and pattern recognition. Finally, illustrative examples are discussed to prove that they can be effectively used to solve problems with uncertainties.
{"title":"Measures of Distance and Entropy Based on Fermatean Fuzzy Type Soft Sets Approach","authors":"M. Kirişci","doi":"10.32323/ujma.1379260","DOIUrl":"https://doi.org/10.32323/ujma.1379260","url":null,"abstract":"This paper introduces the definition of Fermatean fuzzy soft sets and some of its properties. The Fermatean fuzzy soft sets are a parameterized family of Fermatean fuzzy soft sets. Fermatean fuzzy soft sets are a generalization of soft sets. Remarkably, the basic properties and operations of Fermatean soft sets are given. Entropy and distance measures are defined for the Fermatean fuzzy soft sets. Further, we propose two algorithms for the decision-making problem and pattern recognition. Finally, illustrative examples are discussed to prove that they can be effectively used to solve problems with uncertainties.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":" 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628401","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 study, the class of $s$-type $ell_{p}( Phi )$ operators is introduced and it is shown that $L_{p,Phi}$ is a quasi-Banach operator ideal. Also, some other classes are defined by using approximation, Gelfand, Kolmogorov, Weyl, Chang, and Hilbert number sequences. Then, some properties are examined.
{"title":"The New Class $L_{p,Phi}$ of $s$-Type Operators","authors":"Pınar Zengin Alp","doi":"10.32323/ujma.1378917","DOIUrl":"https://doi.org/10.32323/ujma.1378917","url":null,"abstract":"In this study, the class of $s$-type $ell_{p}( Phi )$ operators is introduced and it is shown that $L_{p,Phi}$ is a quasi-Banach operator ideal. Also, some other classes are defined by using approximation, Gelfand, Kolmogorov, Weyl, Chang, and Hilbert number sequences. Then, some properties are examined.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"4 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138585319","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}
Let $pin {Bbb N}$, $s=(s_1,...,s_p)in {Bbb C}^p$, $h=(h_1,...,h_p)in {Bbb R}^p_+$, $(n)=(n_1,...,n_p)in {Bbb N}^p$ and the sequences $lambda_{(n)}=(lambda^{(1)}_{n_1},...,lambda^{(p)}_{n_p})$ are such that $0h}f_{(n)}exp{(lambda_{(n)},s)}$ absolutely converges in $Pi^p_0={s:text{Re},s
让美元 p { Bbb N} $, $ s = (s_1,…,s_p) p { Bbb C} ^ $, $ h = (h_1,…,h_p) { Bbb R} ^ p_ + $, $ (N) = (n_1,…,n_p) p { Bbb N} ^和序列美元lambda_ {(N)} =(λ^ {(1)}_ {n_1},…,λ^ {(p)} _ {n_p}),美元0 h f {(N)}} exp {( lambda_ {(N)}, s) }绝对收敛在美元π^ p_0 = {{你} 文本,s
{"title":"PSEUDOSTARLIKENESS AND PSEUDOCONVEXITY OF MULTIPLE DIRICHLET SERIES","authors":"Myroslav SHEREMETA","doi":"10.32323/ujma.1359248","DOIUrl":"https://doi.org/10.32323/ujma.1359248","url":null,"abstract":"Let $pin {Bbb N}$, $s=(s_1,...,s_p)in {Bbb C}^p$, $h=(h_1,...,h_p)in {Bbb R}^p_+$, $(n)=(n_1,...,n_p)in {Bbb N}^p$ and the sequences $lambda_{(n)}=(lambda^{(1)}_{n_1},...,lambda^{(p)}_{n_p})$ are such that $0h}f_{(n)}exp{(lambda_{(n)},s)}$ absolutely converges in $Pi^p_0={s:text{Re},s","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"33 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136158007","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 study the conchodial surfaces in 3-dimensional Euclidean space with the condition $Delta x_{i}=lambda _{i}x_{i}$ where $Delta $ denotes the Laplace operator with respect to the first fundamental form. We obtain the classification theorem for these surfaces satisfying under this condition. Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.
{"title":"Conchoidal Surfaces in Euclidean 3-space Satisfying $Delta x_{i}=lambda _{i}x_{i}$","authors":"Betül BULCA SOKUR, Tuğçe DİRİM","doi":"10.32323/ujma.1330866","DOIUrl":"https://doi.org/10.32323/ujma.1330866","url":null,"abstract":"In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition $Delta x_{i}=lambda _{i}x_{i}$ where $Delta $ denotes the Laplace operator with respect to the first fundamental form. We obtain the classification theorem for these surfaces satisfying under this condition. Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136277410","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, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected $T_0$-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are presented in terms of asymmetric norms. According to that, we investigated some different aspects and examples of local antisymmetric connectedness in the framework of asymmetrically normed real vector spaces. Specifically, it is proved that the structures of antisymmetric connectedness and local antisymmetric connectedness coincide for the $T_0$-quasi-metrics induced by the asymmetric norms which associate the theory of quasi-metrics with functional analysis.
{"title":"Local Antisymmetric Connectedness in Asymmetrically Normed Real Vector Spaces","authors":"Nezakat JAVANSHIR, Filiz YILDIZ","doi":"10.32323/ujma.1323655","DOIUrl":"https://doi.org/10.32323/ujma.1323655","url":null,"abstract":"In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected $T_0$-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are presented in terms of asymmetric norms. According to that, we investigated some different aspects and examples of local antisymmetric connectedness in the framework of asymmetrically normed real vector spaces. Specifically, it is proved that the structures of antisymmetric connectedness and local antisymmetric connectedness coincide for the $T_0$-quasi-metrics induced by the asymmetric norms which associate the theory of quasi-metrics with functional analysis.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136272369","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}
This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results.
{"title":"On the study of Semilinear Fractional Differential Equations involving Atangana-Baleanu-Caputo derivative","authors":"Samira ZERBİB, Ahmed KAJOUNI","doi":"10.32323/ujma.1288015","DOIUrl":"https://doi.org/10.32323/ujma.1288015","url":null,"abstract":"This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 &lt; theta &lt; 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results.","PeriodicalId":498123,"journal":{"name":"Universal journal of mathematics and applications","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136276677","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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