In this study, a dynamical system to explain a disease model with environmental stress in a general aspect is considered. The model is expressed by the standard differential equations and its Caputo fractional form. We describe a numerical approach based on the numerical technique of Adams-Bashforth-Moulton for the solution of the system of differential equations including the initial conditions. Besides, we indicate briefly the existence, uniqueness, and convergence of the technique. One of the subjects of the study is to contribute with a new design of the present technique to obtain numerical solutions to such problems in the literature which can be investigated for further approximations. Further, we provide the stability analysis around the coexistence equilibrium. Additionally, we illustrate the findings to show the behaviour of the system, time evolution, and the phase plane plots for the specific parameters.
{"title":"A numerical approach for a dynamical system of fractional infectious disease problem","authors":"Burcu Gürbüz, Veysel Fuat Hatipoğlu, Aytül Gökçe","doi":"10.15672/hujms.1314440","DOIUrl":"https://doi.org/10.15672/hujms.1314440","url":null,"abstract":"In this study, a dynamical system to explain a disease model with environmental stress in a general aspect is considered. The model is expressed by the standard differential equations and its Caputo fractional form. We describe a numerical approach based on the numerical technique of Adams-Bashforth-Moulton for the solution of the system of differential equations including the initial conditions. Besides, we indicate briefly the existence, uniqueness, and convergence of the technique. One of the subjects of the study is to contribute with a new design of the present technique to obtain numerical solutions to such problems in the literature which can be investigated for further approximations. Further, we provide the stability analysis around the coexistence equilibrium. Additionally, we illustrate the findings to show the behaviour of the system, time evolution, and the phase plane plots for the specific parameters.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"7 11","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We take into account the first order nonlinear neutral differential equation with distributed deviating arguments. Using Krasnoselskii's fixed point theorem, we give some new criteria for the existence of positive periodic solutions to this equation. The theorems we have established are illustrated by an example.
{"title":"Existence results for positive periodic solutions to first order neutral differential equations with distributed deviating arguments","authors":"T. Candan","doi":"10.15672/hujms.1282490","DOIUrl":"https://doi.org/10.15672/hujms.1282490","url":null,"abstract":"We take into account the first order nonlinear neutral differential equation with distributed deviating arguments. \u0000 Using Krasnoselskii's fixed point theorem, we give some new criteria for the existence of positive periodic solutions to this equation. The theorems we have established are illustrated by an example.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"5 11","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we first construct a new generalization of n-polynomial convex function. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n polynomial convexity. Also, we see that the obtained results in the paper while comparing with Hölder, Hölder-İşcan and power-mean, improved-power-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.
本文首先构建了 n 多项式凸函数的新广义。利用这一构造，我们推导出了这一新广义的某些不等式，并证明了绝对值一阶导数对应于一类新的 n 多项式凸函数。此外，我们还看到，论文中获得的结果在与荷尔德、荷尔德-İşcan 和幂均积分、改进幂均积分不等式进行比较时，显示出这些结果给出了比其他结果更好的方法。最后，我们以包含一些手段的应用结束本文。
{"title":"Construction of a new generalization for n-polynomial convexity with their certain inequalities","authors":"M. Kadakal, I. Işcan, H. Kadakal","doi":"10.15672/hujms.1310861","DOIUrl":"https://doi.org/10.15672/hujms.1310861","url":null,"abstract":"In this paper, we first construct a new generalization of n-polynomial convex function. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n polynomial convexity. Also, we see that the obtained results in the paper while comparing \u0000with Hölder, Hölder-İşcan and power-mean, improved-power-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"80 24","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider generalized product type operators D*nuCϕ and T*n_{u1,u2,ϕ}. Then we provide several characterizations, as equivalent statements, for the boundedness and compactness of these operators between Bloch type spaces Bα(U), for all 0 < α < ∞.
{"title":"Generalized product-type operators between Bloch-type spaces","authors":"Ebrahim Abbasi, Sepideh Nasresfahani̇","doi":"10.15672/hujms.1299653","DOIUrl":"https://doi.org/10.15672/hujms.1299653","url":null,"abstract":"In this paper, we consider generalized product type operators D*nuCϕ and T*n_{u1,u2,ϕ}. Then we \u0000provide several characterizations, as equivalent statements, for the boundedness and compactness of these \u0000operators between Bloch type spaces Bα(U), for all 0 < α < ∞.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"5 11","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce new algorithms for finding a solution of a variational inequality problem involving pseudo-monotone operator which is also a fixed point of a Bregman relatively nonexpansive mapping in p-uniformly convex and uniformly smooth Banach spaces that are more general than Hilbert spaces. We prove weak and strong convergence theorems for proposed algorithms. Finally, we give some numerical experiments for supporting our main results.
{"title":"New algorithms for solving pseudo-monotone variational inequalities in Banach spaces","authors":"G. Zamani Eskandani, M. Raei̇si̇, R. Lotfi̇kar","doi":"10.15672/hujms.1228124","DOIUrl":"https://doi.org/10.15672/hujms.1228124","url":null,"abstract":"In this paper, we introduce new algorithms for finding a solution of a variational \u0000inequality problem involving pseudo-monotone operator which is also a fixed point \u0000of a Bregman relatively nonexpansive mapping in p-uniformly convex and uniformly \u0000smooth Banach spaces that are more general than Hilbert spaces. We prove weak \u0000and strong convergence theorems for proposed algorithms. Finally, we give some \u0000numerical experiments for supporting our main results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 12","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we deal with the initial boundary value problem for a viscoelastic system related to the quasilinear parabolic equation with nonlinear boundary source term on a manifold $mathbb{M}$ with corner singularities. We prove that, under certain conditions on relaxation function $g$, any solution $u$ in the corner-Sobolev space $mathcal{H}^{1,(frac{N-1}{2},frac{N}{2})}_{partial^{0}mathbb{M}}(mathbb{M})$ blows up in finite time. The estimates of the life-span of solutions are also given.
{"title":"Finite-time property of a mechanical viscoelastic system with nonlinear boundary conditions on corner-Sobolev spaces","authors":"Morteza Koozehgar Kalleji","doi":"10.15672/hujms.1286267","DOIUrl":"https://doi.org/10.15672/hujms.1286267","url":null,"abstract":"In this article, we deal with the initial boundary value problem for \u0000a viscoelastic system related to the quasilinear parabolic equation \u0000with nonlinear boundary source term on a manifold $mathbb{M}$ with \u0000corner singularities. We prove that, under certain conditions on \u0000relaxation function $g$, any solution $u$ in the corner-Sobolev \u0000space \u0000$mathcal{H}^{1,(frac{N-1}{2},frac{N}{2})}_{partial^{0}mathbb{M}}(mathbb{M})$ \u0000blows up in finite time. The estimates of the life-span of solutions \u0000are also given.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"6 4","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In [17], the authors established a new semigroup N as an extension of both Rees matrix and completely zero-simple semigroups. In this paper, by taking into account the Zappa-Sz'{e}p product obtained by special subsemigroups of N, we will expose some new distinguishing theoretical results on this product.
在 [17] 中，作者建立了一个新的半群 N，作为里斯矩阵和完全零简单半群的扩展。在本文中，我们将考虑由 N 的特殊子半群得到的 Zappa-Sz'{e}p 乘积，揭示关于该乘积的一些新的显著理论结果。
{"title":"New results over Zappa-Szep products via a recent semigroup","authors":"Nurten URLU ÖZALAN","doi":"10.15672/hujms.1085952","DOIUrl":"https://doi.org/10.15672/hujms.1085952","url":null,"abstract":"In [17], the authors established a new semigroup N as an extension of both Rees matrix and completely zero-simple semigroups. In this paper, by taking into account the Zappa-Sz'{e}p product obtained by special subsemigroups of N, we will expose some new distinguishing theoretical results on this product.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"7 6","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article encompasses the study of non-regular semigroups. First, we show that the $lambda$-semidirect product $M rtimes^{lambda} W$ of a left $P$-Ehresmann semigroup $M$ and a left restriction semigroup $W$ is a left $P$-Ehresmann semigroup. We explore the behavior of generalized Green's relations on $M rtimes^{lambda} W$, and investigate some properties of $M rtimes^{lambda} W$. Second, the Zappa-Szép product of a right Ehresmann semigroup and its distinguished semilattice is studied. Lastly, the theory of representations of left Ehresmann semigroups with zero via homomorphisms of left Ehresmann semigroups with zero into Clifford restriction semigroups with zero is presented.
{"title":"On non-regular semigroups: $lambda$-semidirect products, Zappa-Szép products and representations","authors":"Baddi-Ul Zaman","doi":"10.15672/hujms.1189391","DOIUrl":"https://doi.org/10.15672/hujms.1189391","url":null,"abstract":"This article encompasses the study of non-regular semigroups. First, we show that the $lambda$-semidirect product $M rtimes^{lambda} W$ of a left $P$-Ehresmann semigroup $M$ and a left restriction semigroup $W$ is a left $P$-Ehresmann semigroup. We explore the behavior of generalized Green's relations on $M rtimes^{lambda} W$, and investigate some properties of $M rtimes^{lambda} W$. Second, the Zappa-Szép product of a right Ehresmann semigroup and its distinguished semilattice is studied. Lastly, the theory of representations of left Ehresmann semigroups with zero via homomorphisms of left Ehresmann semigroups with zero into Clifford restriction semigroups with zero is presented.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $Rltimes M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$. We first study how to construct torsion pairs over $Rltimes M$ from torsion pairs over $R$. Some characterizations of finitely generated (presented) modules, flat modules and coherent rings relative to a torsion pair over $Rltimes M$ are obtained. Then we discuss the transfers of torsion pairs over $Rltimes M$ to $R$. Finally, some applications are given in Morita context rings.
{"title":"Torsion pairs and related modules over trivial ring extensions","authors":"Lixin Mao","doi":"10.15672/hujms.1272122","DOIUrl":"https://doi.org/10.15672/hujms.1272122","url":null,"abstract":"Let $Rltimes M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$. We first study how to construct torsion pairs over $Rltimes M$ from torsion pairs over $R$. Some characterizations of finitely generated (presented) modules, flat modules and coherent rings relative to a torsion pair over $Rltimes M$ are obtained. Then we discuss the transfers of torsion pairs over $Rltimes M$ to $R$. Finally, some applications are given in Morita context rings.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"4 9","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $psi in H(BB_n),$ the space of all holomorphic functions on the unit ball $BB_n$ of $C^n,$ $varphi = (varphi_1, ldots, varphi_n) in S(BB_n)$ the set of holomorphic self-maps of $BB_n.$ Let $C_{psi, varphi}: mathcal B_{nu}$ (and $ mathcal B_{nu,0}$) $to mathcal B_{mu} $ (and $ mathcal B_{mu,0}$) be weighted extended Ces`aro operators induced by products of the extended Ces`aro operator $ C_varphi $ and integral operator $T_psi.$ In this paper, we characterize the boundedness and compactness of $ C_{psi,varphi} $ via the estimates for either $ |varphi| $ or $ |varphi_k| $ textit{for some $ kin {1,ldots,n}. $} At the same time, we also give the asymptotic estimates of the norms of these operators.
让 $psi in H(BB_n),$ $C^n 的单位球 $BB_n$ 上所有全态函数的空间，$varphi = (varphi_1, ldots, varphi_n)in S(BB_n)$ $ $BB_n 的全态自映射的集合：(and $ mathcal B_{nu}$) $to mathcal B_{mu} $ (and $ mathcal B_{mu,0}$) be weighted extended Ces`aro operators induced by the products of the extended Ces`aro operator $ C_varphi $ and integral operator $T_psi.在本文中，我们通过对 $ |varphi| $ 或 $ |varphi_k| $ 的估计来描述 $ C_{psi,varphi} $ 的有界性和紧凑性。$}同时，我们还给出了这些算子规范的渐近估计值。
{"title":"On the boundedness and compactness of extended Ces`aro composition operators between weighted Bloch-type spaces","authors":"Lien VUONG LAM, Thai THUAN QUANG","doi":"10.15672/hujms.1197627","DOIUrl":"https://doi.org/10.15672/hujms.1197627","url":null,"abstract":"Let $psi in H(BB_n),$ the space of all holomorphic functions on the unit ball $BB_n$ of $C^n,$ $varphi = (varphi_1, ldots, varphi_n) in S(BB_n)$ the set of holomorphic self-maps of $BB_n.$ Let $C_{psi, varphi}: mathcal B_{nu}$ (and $ mathcal B_{nu,0}$) $to mathcal B_{mu} $ (and $ mathcal B_{mu,0}$) be weighted extended Ces`aro operators induced \u0000 by products of the extended Ces`aro operator $ C_varphi $ and integral operator $T_psi.$ \u0000 In this paper, we characterize the boundedness and compactness of $ C_{psi,varphi} $ via the estimates for either $ |varphi| $ or $ |varphi_k| $ textit{for some $ kin {1,ldots,n}. $} At the same time, we also give the asymptotic estimates of the norms of these operators.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"10 8","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139439813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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