Pub Date : 2024-07-10DOI: 10.5556/j.tkjm.56.2025.5268
Jose Raul Quintero Henao
In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.
在本文中，我们重新探讨了 N = 1、2、3 的 Benney-Roskes 系统（也称为 Zakharov-Rubenchik 系统）的好求解性，并利用哈密顿结构和 Liapunov 方法诱导的变分法，建立了 N = 1 情况下基态驻波的非线性轨道稳定性。
{"title":"On the well-posedness and stability analysis of standing waves for a 1D-Benney-Roskes system","authors":"Jose Raul Quintero Henao","doi":"10.5556/j.tkjm.56.2025.5268","DOIUrl":"https://doi.org/10.5556/j.tkjm.56.2025.5268","url":null,"abstract":"In this paper, we revisit the well-posedness for the Benney-Roskes system (also known as Zakharov-Rubenchik systems) for N = 1, 2, 3, and establish the nonlinear orbital stability of ground state standing waves in the case N = 1, by using the variational approach induced by the Hamiltonian structure and the Liapunov method.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141835642","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 : 2024-05-05DOI: 10.5556/j.tkjm.56.2025.5222
Nidhi R. Joshi, B. I. Dave
The work incorporates a generalization of the Legendre polynomial by introducing a parameter $p>0$ in its generating function. The coefficients thus generated, constitute a class of the polynomials which are termed as the $p$-Legendre polynomials. It is shown that this class turns out to be orthogonal with respect to the weight function: $(1-sqrt{p} x)^{frac{p+1}{2p}-1}(1+sqrt{p} x)^{frac{p+1}{2p}-1}$ over the interval $(-frac{1}{sqrt{p}}, frac{1}{sqrt{p}}).$ Among the other properties derived, include the Rodrigues formula, normalization, recurrence relation and zeros. A graphic depiction for $p=0.5, 1, 2,$ and $3$ is shown. The $p$-Legendre polynomials are used to estimate a function using the least squares approach. The approximations are graphically depicted for $p=0.7, 1, 2.$
{"title":"An orthogonal class of $p$-Legendre polynomials on variable interval","authors":"Nidhi R. Joshi, B. I. Dave","doi":"10.5556/j.tkjm.56.2025.5222","DOIUrl":"https://doi.org/10.5556/j.tkjm.56.2025.5222","url":null,"abstract":"The work incorporates a generalization of the Legendre polynomial by introducing a parameter $p>0$ in its generating function. The coefficients thus generated, constitute a class of the polynomials which are termed as the $p$-Legendre polynomials. It is shown that this class turns out to be orthogonal with respect to the weight function: $(1-sqrt{p} x)^{frac{p+1}{2p}-1}(1+sqrt{p} x)^{frac{p+1}{2p}-1}$ over the interval $(-frac{1}{sqrt{p}}, frac{1}{sqrt{p}}).$ Among the other properties derived, include the Rodrigues formula, normalization, recurrence relation and zeros. A graphic depiction for $p=0.5, 1, 2,$ and $3$ is shown. The $p$-Legendre polynomials are used to estimate a function using the least squares approach. The approximations are graphically depicted for $p=0.7, 1, 2.$","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141012106","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 : 2024-03-29DOI: 10.5556/j.tkjm.56.2025.5261
Pragati Gautam, Chanpreet Kaur
This paper is aimed at proving the efficiency of a faster iterative scheme called $PC^*$-iterative scheme to approximate the fixed points for the class of Suzuki's Generalized non-expansive mapping in a uniformly convex Banach space. We will prove some weak and strong convergence results. It is justified numerically that the $PC^*$-iterative scheme converges faster than many other remarkable iterative schemes. We will also provide numerical illustrations with graphical representations to prove the efficiency of $PC^*$ iterative scheme. As an application of the solution of a fractional differential equation is obtained by using $PC^*$ iterative scheme.
{"title":"Approximating the fixed points of Suzuki's generalized non-expansive map via an efficient iterative scheme with an application","authors":"Pragati Gautam, Chanpreet Kaur","doi":"10.5556/j.tkjm.56.2025.5261","DOIUrl":"https://doi.org/10.5556/j.tkjm.56.2025.5261","url":null,"abstract":"This paper is aimed at proving the efficiency of a faster iterative scheme called $PC^*$-iterative scheme to approximate the fixed points for the class of Suzuki's Generalized non-expansive mapping in a uniformly convex Banach space. We will prove some weak and strong convergence results. It is justified numerically that the $PC^*$-iterative scheme converges faster than many other remarkable iterative schemes. We will also provide numerical illustrations with graphical representations to prove the efficiency of $PC^*$ iterative scheme. As an application of the solution of a fractional differential equation is obtained by using $PC^*$ iterative scheme.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368288","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 : 2024-03-20DOI: 10.5556/j.tkjm.55.2024.5276
Ricardo Córdoba Gómez, Anyi Daniela Corredor
In this work, using an appropriate Carleman-type estimate, we establish a unique continuation result for the Rosenau equation that models the dynamics of dense discrete systems with high order effects.
{"title":"Unique continuation property for the Rosenau equation","authors":"Ricardo Córdoba Gómez, Anyi Daniela Corredor","doi":"10.5556/j.tkjm.55.2024.5276","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5276","url":null,"abstract":"In this work, using an appropriate Carleman-type estimate, we establish a unique continuation result for the Rosenau equation that models the dynamics of dense discrete systems with high order effects.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140388904","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 introduce a method for finding common solution of variational inequality, finite family of monotone inclusion and fixed point problems of demicontractive mappings in a real Hilbert space. We prove strong convergence result of proposed method. We also provide a numerical example to show that our method is efficient from the numerical point of view.
{"title":"A novel iterative algorithm for solving variational inequality, finite family of monotone inclusion and fixed point problems","authors":"Seema Anjali, Renu Mehra, Chugh Charu, Batra, S. Mehra, Charu Batra","doi":"10.5556/j.tkjm.55.2024.5138","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5138","url":null,"abstract":"In this paper, we introduce a method for finding common solution of variational inequality, finite family of monotone inclusion and fixed point problems of demicontractive mappings in a real Hilbert space. We prove strong convergence result of proposed method. We also provide a numerical example to show that our method is efficient from the numerical point of view.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140493104","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 : 2023-11-30DOI: 10.5556/j.tkjm.55.2024.5158
Medjahed Djilali, Khellaf Ould Melha, V. L. Chinchane
In this paper, the extended Jacobi elliptic function expansion method is applied to conformable time-fractional Sasa-Satsumaequation. Variety of new traveling wave solutions are constructed. Thanks to the Mathematica software package, to interprete the behavior of some particular exact solutions, surfaces and contour plots are plotted.
{"title":"Various new traveling wave solutions for conformable time-fractional Sasa-Satsuma equation","authors":"Medjahed Djilali, Khellaf Ould Melha, V. L. Chinchane","doi":"10.5556/j.tkjm.55.2024.5158","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5158","url":null,"abstract":"In this paper, the extended Jacobi elliptic function expansion method is applied to conformable time-fractional Sasa-Satsumaequation. Variety of new traveling wave solutions are constructed. Thanks to the Mathematica software package, to interprete the behavior of some particular exact solutions, surfaces and contour plots are plotted.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139205605","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 : 2023-11-14DOI: 10.5556/j.tkjm.55.2024.5172
Pradeep Kumar, Anju Panwar
In this paper, a common solution of fixed point and generalized equilibrium problems using an asymptotically nonexpansive mapping is determined via iterative approach. Further, an application and numerical example of the main result are given.
{"title":"Common solutions of fixed point and generalized equilibrium problems using asymptotically nonexpansive mapping","authors":"Pradeep Kumar, Anju Panwar","doi":"10.5556/j.tkjm.55.2024.5172","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5172","url":null,"abstract":"In this paper, a common solution of fixed point and generalized equilibrium problems using an asymptotically nonexpansive mapping is determined via iterative approach. Further, an application and numerical example of the main result are given.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134901559","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 the present work, we developed a deterministic SHATR (Susceptible - HIV infected -AIDS infected - Antiretroviral Treatment - Recovered) compartment model for HIV/AIDS. This model considers the disease outbreak due to a lack of awareness and treatment. The steady states of the proposed model system are obtained and analyzed by using the nonlinear stability theory of differential equations. The basic reproduction number is derived and explored to determine the stability and sensitivity index of some important relative parameters. Further, to know the global behavior of the model one parameter bifurcation study is discussed. Moreover, the optimal control theory has been applied to identify the optimal strategy by taking treatment and awareness for safe intercourse as control parameters. The control problem is solved analytically by using Pontryagin’s maximum principle. Finally, the model is simulated to describe the optimality under various assumptions and the stability of equilibrium points.
{"title":"Mathematical modeling and optimal control of a deterministic SHATR model of HIV/AIDS with possibility of rehabilitation: a dynamic analysis","authors":"Pankaj Singh Rana, Nitin Sharma, Anupam Priyadarshi","doi":"10.5556/j.tkjm.55.2024.5109","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5109","url":null,"abstract":"In the present work, we developed a deterministic SHATR (Susceptible - HIV infected -AIDS infected - Antiretroviral Treatment - Recovered) compartment model for HIV/AIDS. This model considers the disease outbreak due to a lack of awareness and treatment. The steady states of the proposed model system are obtained and analyzed by using the nonlinear stability theory of differential equations. The basic reproduction number is derived and explored to determine the stability and sensitivity index of some important relative parameters. Further, to know the global behavior of the model one parameter bifurcation study is discussed. Moreover, the optimal control theory has been applied to identify the optimal strategy by taking treatment and awareness for safe intercourse as control parameters. The control problem is solved analytically by using Pontryagin’s maximum principle. Finally, the model is simulated to describe the optimality under various assumptions and the stability of equilibrium points.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135469938","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 article, we demonstrate some fixed point results that generalises the Banachcontraction principle in a different way from the previously established literature findings. Weprovide some fixed point findings for non linear F type contractions in Strong Partial b-MetricSpaces (SPbMS). We also include some examples that demonstrates the applicability of ourfindings.
{"title":"Some fixed point results for nonlinear $F$-type contractions in strong partial b-metric spaces","authors":"None Savita Rathee, None Neelam Kumari, Monika Swami","doi":"10.5556/j.tkjm.55.2024.5145","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5145","url":null,"abstract":"In this article, we demonstrate some fixed point results that generalises the Banachcontraction principle in a different way from the previously established literature findings. Weprovide some fixed point findings for non linear F type contractions in Strong Partial b-MetricSpaces (SPbMS). We also include some examples that demonstrates the applicability of ourfindings.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135686330","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 : 2023-08-30DOI: 10.5556/j.tkjm.55.2024.5118
Bang-Yen Chen, Shihshu Walter Wei
By studying cohomology classes that are related with n-harmonic morphisms and F-harmonic maps, we augment and extend several results on F-harmonic maps, harmonic maps in [1, 3, 14], p-harmonic morphisms in [17], and also revisit our previous results in [9, 10, 21] on Riemannian submersions and n-harmonic morphisms which are submersions. The results, for example Theorem 3.2 obtaine by utilizing the n-conservation law (2.6), are sharp.
{"title":"$n$-harmonicity, minimality, conformality and cohomology","authors":"Bang-Yen Chen, Shihshu Walter Wei","doi":"10.5556/j.tkjm.55.2024.5118","DOIUrl":"https://doi.org/10.5556/j.tkjm.55.2024.5118","url":null,"abstract":"
 
 
 By studying cohomology classes that are related with n-harmonic morphisms and F-harmonic maps, we augment and extend several results on F-harmonic maps, harmonic maps in [1, 3, 14], p-harmonic morphisms in [17], and also revisit our previous results in [9, 10, 21] on Riemannian submersions and n-harmonic morphisms which are submersions. The results, for example Theorem 3.2 obtaine by utilizing the n-conservation law (2.6), are sharp.
 
 
","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136162288","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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