Pub Date : 2023-05-03DOI: 10.5556/j.tkjm.55.2024.5079
N. Kumari
In this study, PPF dependent fixed point theorems are proved for a nonlinear operator, where the domain space $C[[a, b], E]$ is distinct from the range space, $E$, which is a Strong Partial b-metric space (SPbMS). We obtain existence and uniqueness of PPF dependent fixed point results for the defined mappings under SPbMS. Our results are the extension of fixed point results in SPbMS. Examples are provided in the support of results.
{"title":"Fixed point theorems with PPF dependence in strong partial b-metric spaces","authors":"N. Kumari","doi":"10.5556/j.tkjm.55.2024.5079","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5079","url":null,"abstract":"In this study, PPF dependent fixed point theorems are proved for a nonlinear operator, where the domain space $C[[a, b], E]$ is distinct from the range space, $E$, which is a Strong Partial b-metric space (SPbMS). We obtain existence and uniqueness of PPF dependent fixed point results for the defined mappings under SPbMS. Our results are the extension of fixed point results in SPbMS. Examples are provided in the support of results.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75784832","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 : 2023-05-01DOI: 10.5556/j.tkjm.54.2023.3988
S. Dragomir
Some fundamental inequalities for Lerch transcendent function with positive terms by utilising certain classical results due to Hölder, Čebyšev, Grüss and others, are established. Some particular cases of interest for Polylogarithm function, Hurwitz zeta function and Legendre chi function are also given.
{"title":"Inequalities for Lerch transcendent function","authors":"S. Dragomir","doi":"10.5556/j.tkjm.54.2023.3988","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.3988","url":null,"abstract":"Some fundamental inequalities for Lerch transcendent function with positive terms by utilising certain classical results due to Hölder, Čebyšev, Grüss and others, are established. Some particular cases of interest for Polylogarithm function, Hurwitz zeta function and Legendre chi function are also given.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79000157","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 : 2023-04-28DOI: 10.5556/j.tkjm.55.2024.5028
Nevin Ertuu{g} G"{u}rb"{u}z, D. Yoon
In this paper, we introduce the type-2 and the type-3 Positional Adapted Frame(PAF) of spacelike curve and timelike curve inMinkowski 3-space. From these PAFs, we study the evolutions of the electric field vectors of the type-2 and type-3 PAFs.As a result, we also investigate the Fermi-Walker parallel and the Lorentz force equation of the electric field vectors for the type-2 and type-3 PAFs in Minkowski 3-space.
{"title":"The evolution of the electric field along optical fiber with respect to the type-2 and 3 PAFs in Minkowski 3-space","authors":"Nevin Ertuu{g} G\"{u}rb\"{u}z, D. Yoon","doi":"10.5556/j.tkjm.55.2024.5028","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5028","url":null,"abstract":"In this paper, we introduce the type-2 and the type-3 Positional Adapted Frame(PAF) of spacelike curve and timelike curve inMinkowski 3-space. From these PAFs, we study the evolutions of the electric field vectors of the type-2 and type-3 PAFs.As a result, we also investigate the Fermi-Walker parallel and the Lorentz force equation of the electric field vectors for the type-2 and type-3 PAFs in Minkowski 3-space.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87625306","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 : 2023-04-26DOI: 10.5556/j.tkjm.55.2024.5097
Mebarka Sattaf, Brahim Khaldi
We study the following singular Kirchhoff type problem [left( Pright) left{ begin{array} [c]{c} -mleft({displaystyleintlimits_{Omega}}leftvert nabla urightvert ^{2}dxright) Delta u=hleft( uright) frac{e^{alpha u^{2}}}{leftvert xrightvert ^{beta}}text{ in} Omega, u=0 text{on}; partialOmega end{array} right. ] where $Omegasubsetmathbb{R}^{2}$ is a bounded domain with smooth boundary and $0inOmega,$ $betainleft[ 0,2right)$, $alpha>0$ and $m$ is a continuous function on $mathbb{R}^{+}.$ Here, $h$ is a suitable preturbation of $e^{alpha u^{2}}$ as $urightarrowinfty.$ In this paper, we prove the existence of solutions of $(P)$. Our tools are Trudinger-Moser inequality with a singular weight and the mountain pass theorem
{"title":"On a class of Kirchhoff type problems with singular exponential nonlinearity","authors":"Mebarka Sattaf, Brahim Khaldi","doi":"10.5556/j.tkjm.55.2024.5097","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5097","url":null,"abstract":"We study the following singular Kirchhoff type problem \u0000[left( Pright) left{ \u0000begin{array} [c]{c} \u0000-mleft({displaystyleintlimits_{Omega}}leftvert nabla urightvert ^{2}dxright) Delta u=hleft( uright) \u0000frac{e^{alpha u^{2}}}{leftvert xrightvert ^{beta}}text{ in} Omega, \u0000u=0 text{on}; partialOmega \u0000end{array} right. \u0000] \u0000where $Omegasubsetmathbb{R}^{2}$ is a bounded domain with smooth boundary and $0inOmega,$ $betainleft[ 0,2right)$, $alpha>0$ and $m$ is a continuous function \u0000on $mathbb{R}^{+}.$ Here, $h$ is a suitable preturbation of $e^{alpha u^{2}}$ as $urightarrowinfty.$ In this paper, we prove the existence of solutions of \u0000$(P)$. Our tools are Trudinger-Moser inequality with a singular weight and the mountain pass theorem","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"88 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76265564","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 : 2023-03-31DOI: 10.5556/j.tkjm.55.2024.5120
M. A. Pathan, M. Shahwan, M. Bin-Saad
Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type extended zeta function together with related integral representations, differential relations, finite sums, and series expansions. Also, we present a relationship between the extended zeta function and the Laguerre polynomials. Our hypergeometric type extended zeta function involves several known zeta functions including the Riemann, Hurwitz, Hurwitz-Lerch, and Barnes zeta functions as particular cases.
{"title":"Hypergeometric type extended bivariate zeta function","authors":"M. A. Pathan, M. Shahwan, M. Bin-Saad","doi":"10.5556/j.tkjm.55.2024.5120","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5120","url":null,"abstract":"Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type extended zeta function together with related integral representations, differential relations, finite sums, and series expansions. Also, we present a relationship between the extended zeta function and the Laguerre polynomials. Our hypergeometric type extended zeta function involves several known zeta functions including the Riemann, Hurwitz, Hurwitz-Lerch, and Barnes zeta functions as particular cases.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81918950","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 : 2023-03-28DOI: 10.5556/j.tkjm.55.2024.5031
A. Ayoade, N. Nyerere, M. Ibrahim
Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , $R_{0}$ , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.
{"title":"An epidemic model for control and possible elimination of Lassa fever","authors":"A. Ayoade, N. Nyerere, M. Ibrahim","doi":"10.5556/j.tkjm.55.2024.5031","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5031","url":null,"abstract":"Lassa fever is a deadly viral disease whose incubation period ranges from six to twenty-one days and about eighty percent of Lassa virus infection is asymptomatic. A deterministic model was formulated to quantify the transmission dynamics of the disease under isolation and treatment of the isolated asymptomatic and symptomatic humans for effective management and possible elimination of the disease. The solutions of the model were shown to be positive and bounded. Equilibrium analysis was conducted and both the disease-free and the endemic equilibria were derived. The threshold quantity for disease elimination , $R_{0}$ , was also obtained and used to derive conditions for the existence of stability of the eqilibria. The quantity was also employed to examine the sensitivity of the model parameters to disease propagation and reduction. The theoretical analysis was then complemented with the quantitative analysis by adopting a set of realistic values for the model parameters in order to show the effect of isolation and treatment on the spread and fatality of Lassa fever. Results from the quantitative study showed that death and infection from Lassa fever fell continuously as more and more exposed individuals were detected and isolated for treatment. The study therefore suggested that any measure taken to eradicate or curtail Lassa fever spread should include detection and isolation of the exposed humans for prompt treatments.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79241851","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 : 2023-03-26DOI: 10.5556/j.tkjm.55.2024.4821
C. Feng
In this paper, a class of nonlinear predator-prey models with three discrete delays is considered. By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system, two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays. Some numerical simulations are provided to illustrate our theoretical prediction.
{"title":"Existence of positive periodic solutions for a predator-prey model","authors":"C. Feng","doi":"10.5556/j.tkjm.55.2024.4821","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.4821","url":null,"abstract":"In this paper, a class of nonlinear predator-prey models with three discrete delays is considered.\u0000By linearizing the system at the positive equilibrium point and analyzing the instability of the linearized system,\u0000two sufficient conditions to guarantee the existence of positive periodic solutions of the system are obtained.\u0000It is found that under suitable conditions on the parameters, time delay affects the stability of the system.\u0000The present method does not need to consider a bifurcating equation which is very complex for such a predator-prey model with three discrete delays.\u0000Some numerical simulations are provided to illustrate our theoretical prediction.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88939022","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 : 2023-03-15DOI: 10.5556/j.tkjm.55.2024.5066
Gizem Koprulu Karakas, B. Şahin
The purpose of this paper is to study triharmonic curves along Riemannian submersions from Riemannian manifolds onto Riemannian manifolds. We obtain necessary and sufficient conditions for a triharmonic curve on the total manifoldof Riemannian submersion from a space form ( respectively, a complex space form) to a Riemannian manifold to be triharmonic curve on the base manifold. The above research problem is also studied in the complex setting of the manifoldon which the Riemannian submersion is defined. In addition, we give several results involving curvature conditions for a triharmonic curves along Riemannian submersions.
{"title":"Triharmonic curves along Riemannian submersions","authors":"Gizem Koprulu Karakas, B. Şahin","doi":"10.5556/j.tkjm.55.2024.5066","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5066","url":null,"abstract":"The purpose of this paper is to study triharmonic curves along Riemannian submersions from Riemannian manifolds onto Riemannian manifolds. We obtain necessary and sufficient conditions for a triharmonic curve on the total manifoldof Riemannian submersion from a space form ( respectively, a complex space form) to a Riemannian manifold to be triharmonic curve on the base manifold. The above research problem is also studied in the complex setting of the manifoldon which the Riemannian submersion is defined. In addition, we give several results involving curvature conditions for a triharmonic curves along Riemannian submersions.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76738754","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 : 2023-03-13DOI: 10.5556/j.tkjm.55.2024.3913
L. Saha
For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $displaystylemax_{vin V(G)}f(v)$ and the emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $displaystylemin_{f}{~span_f(G)}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $kin{n-1, n-2,n-3}$ in different approach but simple way.
{"title":"A different approach for multi-level distance labellings of path structure networks","authors":"L. Saha","doi":"10.5556/j.tkjm.55.2024.3913","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.3913","url":null,"abstract":"For a positive integer $k$, a radio $k$-labelling of a simple connected graph $G=(V, E)$ is a mapping $f$ from the vertex set $V(G)$ to a set of non-negative integers such that $|f(u)-f(v)|geqslant k+1-d(u,v)$ for each pair of distinct vertices $u$ and $v$ of $G$, where $d(u,v)$ is the distance between $u$ and $v$ in $G$. The emph{span} of a radio $k$-coloring $f$, denoted by $span_f(G)$, is defined as $displaystylemax_{vin V(G)}f(v)$ and the emph{radio $k$-chromatic number of $G$}, denoted by $rc_k(G)$, is $displaystylemin_{f}{~span_f(G)}$ where the minimum is taken over all radio $k$-labellings of $G$. In this article, we present results of radio $k$-chromatic number of path $P_n$ for $kin{n-1, n-2,n-3}$ in different approach but simple way.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"80 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76828829","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 : 2022-11-15DOI: 10.5556/j.tkjm.54.2023.4954
Foko Kamseu Maturin, D. David, Abel Nguelemo Kenfack, Woukeng Jean Louis
This paper provide evidence of the existence and uniqueness result for the viscosity solutions of inhomogeneous Vlasov equation. we consider the Cauchy-Dirichlet problem for the relativistic Vlasov equation with near vacuum initial data where the distribution function depends on the time, the position, the momentum and the non-Abelian charge of particles. We consider this equation on aSchwarzschild outer space-time with Yang-Mills field.
{"title":"Viscosity solutions for the relativistic inhomogeneous Vlasov equation in Schwarzschild outer space-time in the presence of the Yang-Mills field","authors":"Foko Kamseu Maturin, D. David, Abel Nguelemo Kenfack, Woukeng Jean Louis","doi":"10.5556/j.tkjm.54.2023.4954","DOIUrl":"https://doi.org/10.5556/j.tkjm.54.2023.4954","url":null,"abstract":"This paper provide evidence of the existence and uniqueness result for the viscosity solutions of inhomogeneous Vlasov equation. we consider the Cauchy-Dirichlet problem for the relativistic Vlasov equation with near vacuum initial data where the distribution function depends on the time, the position, the momentum and the non-Abelian charge of particles. We consider this equation on aSchwarzschild outer space-time with Yang-Mills field.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75444667","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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