The intention of this script is to construct and obtain some new results for common coupled fixed points in b-metric space for a pair of mappings satisfying rational type contraction. The present results extend, modify, and generalize the existing literature. The results are verified with the help of suitable examples.
{"title":"Rational Type Contraction in b-Metric Spaces and Common Coupled Fixed Point Theorems","authors":"S. K. Tiwari, Jayant Prakash Ganvir, S. K. Sahani","doi":"10.3126/jnms.v6i1.57410","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57410","url":null,"abstract":"The intention of this script is to construct and obtain some new results for common coupled fixed points in b-metric space for a pair of mappings satisfying rational type contraction. The present results extend, modify, and generalize the existing literature. The results are verified with the help of suitable examples.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124648366","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}
The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ +b−1)−z(θ +a)]w = 0. Kummer’s first formula and Kummer’s second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w1(z), w2(z), w3(z), w4(z), w5(z) and w6(z) as the combination of three solutions.
{"title":"Kummer’s Theorems, Popular Solutions and Connecting Formulas on Hypergeometric Function","authors":"Madhav Poudel, H. Harsh, N. Pahari, D. Panthi","doi":"10.3126/jnms.v6i1.57413","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57413","url":null,"abstract":"The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ +b−1)−z(θ +a)]w = 0. Kummer’s first formula and Kummer’s second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w1(z), w2(z), w3(z), w4(z), w5(z) and w6(z) as the combination of three solutions.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122459351","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}
There are many probability models describing the time related events data. In this study, the exponential distribution is modified by adding one more parameter to get more flexible probability model called Extended Kumaraswamy Exponential (EKwE) distribution using the New Kw-G family (NKwG) of distributions. We have studied some of the statistical characteristics of the model, such as its reliability function, hazard rate function, and quantile function. For testing the applicability of the model, a real data set based on COVID-19 data is taken. The Cramer-von Mises (CVM) approach, Least Square Estimation (LSE), and Maximum Likelihood Estimation (MLE) are used to estimate the model’s parameters. Validity of the model is checked by using P-P plot and Q-Q plot. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Information Criterion (HQIC) are also used for model comparison. Goodness of fit of the proposed model is tested using Kolmogrov-Smirnov (KS), Cramer-Von Mises (CVM) and Anderson-Darling (An) test statistics along with respective p-values. All the analysis of the study is performed by using R programming.
{"title":"Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set","authors":"A. Chaudhary, Lal Babu Sah Telee, Vijay Kumar","doi":"10.3126/jnms.v6i1.57657","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57657","url":null,"abstract":"There are many probability models describing the time related events data. In this study, the exponential distribution is modified by adding one more parameter to get more flexible probability model called Extended Kumaraswamy Exponential (EKwE) distribution using the New Kw-G family (NKwG) of distributions. We have studied some of the statistical characteristics of the model, such as its reliability function, hazard rate function, and quantile function. For testing the applicability of the model, a real data set based on COVID-19 data is taken. The Cramer-von Mises (CVM) approach, Least Square Estimation (LSE), and Maximum Likelihood Estimation (MLE) are used to estimate the model’s parameters. Validity of the model is checked by using P-P plot and Q-Q plot. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Information Criterion (HQIC) are also used for model comparison. Goodness of fit of the proposed model is tested using Kolmogrov-Smirnov (KS), Cramer-Von Mises (CVM) and Anderson-Darling (An) test statistics along with respective p-values. All the analysis of the study is performed by using R programming.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125882333","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 K ⊂ Z+ and define the set H∞K (D) to be the collection of all bounded analytic functions on the unit disk D in the complex plane whose kth derivative vanishes at zero for all k ∈ K. Depending on the choice of K, the set H∞K (D) may or may not be an algebra. We consider the case where K is infinite and show how to construct these sets.
{"title":"Characterization of Sets K for which H∞ K (D) is an Algebra - Part II","authors":"D. Banjade, Jeremiah Dunivin","doi":"10.3126/jnms.v6i1.57414","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57414","url":null,"abstract":"Let K ⊂ Z+ and define the set H∞K (D) to be the collection of all bounded analytic functions on the unit disk D in the complex plane whose kth derivative vanishes at zero for all k ∈ K. Depending on the choice of K, the set H∞K (D) may or may not be an algebra. We consider the case where K is infinite and show how to construct these sets.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"194 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134405320","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}
The work on frame theory has undergone a remarkable evolution over the last century. Several related properties have applications on many fields of mathematics, engineering, signal and image processing, informatics, medecine and probability. In order to search for new results related to the role of operators in frame theory using the characterization of the positive elements in a C∗-algebra, we introduce the concept of positive operator frame, L-positive operator frame, ∗-positive operator frame and ∗-L-positive operator frame for the set of all adjointable operators on a Hilbert C∗-module denoted End∗B(H) where L is a positive operator. Also, we give some new properties.
在过去的一个世纪里，框架理论的研究经历了显著的发展。一些相关的性质在数学、工程、信号和图像处理、信息学、医学和概率论的许多领域都有应用。为了利用C * -代数中正元素的表征寻找算子在框架理论中作用的新结果，我们为Hilbert C * -模上的所有可伴算子集合引入了正算子框架、L-正算子框架、∗-正算子框架和∗-L-正算子框架的概念，其中L是一个正算子。同时，我们给出了一些新的属性。
{"title":"Positive Operator Frame for Hilbert C*-modules","authors":"H. Labrigui, Hafida Massit, M. Rossafi","doi":"10.3126/jnms.v6i1.57469","DOIUrl":"https://doi.org/10.3126/jnms.v6i1.57469","url":null,"abstract":"The work on frame theory has undergone a remarkable evolution over the last century. Several related properties have applications on many fields of mathematics, engineering, signal and image processing, informatics, medecine and probability. In order to search for new results related to the role of operators in frame theory using the characterization of the positive elements in a C∗-algebra, we introduce the concept of positive operator frame, L-positive operator frame, ∗-positive operator frame and ∗-L-positive operator frame for the set of all adjointable operators on a Hilbert C∗-module denoted End∗B(H) where L is a positive operator. Also, we give some new properties.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130850799","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}
Rabies is a dangerous disease that kills many people than any other communicable disease and yet it is underrated. This results from the little knowledge on the myriad ways of transmission of the virus. A deterministic model is proposed to study the spread of the rabies virus in both domestic dogs (Canis familiaries) and humans (Homo sapiens). We elaborately studied the spread of the rabies virus from dogs to-dogs, dogs-to-humans and for the first time, humans-to-humans. Sensitivity analysis is performed to determine the influence of various parameters on the transmission of rabies the most. The rabies-free equilibrium and the endemic equilibrium points were determined and the conditions under which the equilibria are stable were also obtained. The stability conditions provide the conditions under which the disease will persist or get to be eradicated. Numerical solutions of the model were obtained using the ode45 routine in MATLAB. The study demonstrated that for rabies to be eradicated, the rate at which dogs are recruited must be decreased, culling of exposed and infected dogs should be increased and mass vaccination of the dog population should be targeted.
{"title":"Mathematical Analysis of Rabies Transmission Dynamics and Control","authors":"Suleman Adamu Bukari, Baba Seidu, M. I. Daabo","doi":"10.3126/jnms.v5i2.50021","DOIUrl":"https://doi.org/10.3126/jnms.v5i2.50021","url":null,"abstract":"Rabies is a dangerous disease that kills many people than any other communicable disease and yet it is underrated. This results from the little knowledge on the myriad ways of transmission of the virus. A deterministic model is proposed to study the spread of the rabies virus in both domestic dogs (Canis familiaries) and humans (Homo sapiens). We elaborately studied the spread of the rabies virus from dogs to-dogs, dogs-to-humans and for the first time, humans-to-humans. Sensitivity analysis is performed to determine the influence of various parameters on the transmission of rabies the most. The rabies-free equilibrium and the endemic equilibrium points were determined and the conditions under which the equilibria are stable were also obtained. The stability conditions provide the conditions under which the disease will persist or get to be eradicated. Numerical solutions of the model were obtained using the ode45 routine in MATLAB. The study demonstrated that for rabies to be eradicated, the rate at which dogs are recruited must be decreased, culling of exposed and infected dogs should be increased and mass vaccination of the dog population should be targeted.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124585355","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}
Present paper is the study about Stancu type generalization of modified Beta-Szasz operators and their q-analogues. We obtain some approximation properties for these operators and estimate the rate of convergence by using the first and second order modulus of continuity. Author also investigates the statistical approximation properties of the q-Beta-Stancu operators using Korokvin theorem.
{"title":"Approximation by Some Stancu Type Linear Positive Operators","authors":"P. Sharma","doi":"10.3126/jnms.v5i2.50017","DOIUrl":"https://doi.org/10.3126/jnms.v5i2.50017","url":null,"abstract":"Present paper is the study about Stancu type generalization of modified Beta-Szasz operators and their q-analogues. We obtain some approximation properties for these operators and estimate the rate of convergence by using the first and second order modulus of continuity. Author also investigates the statistical approximation properties of the q-Beta-Stancu operators using Korokvin theorem.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122956048","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 aims to understand and predict the dynamics of spread of COVID-19. It is based on government data on COVID-19 from February 1, 2021 to August 31, 2021. First, Vector Autoregression (VAR) model is used here to model the interrelationships between time series data of daily tested, infected, dead and discharged. The impact of under-reporting on interrelated variables is quantified. The behavior of the parameters of these VAR model is also analyzed. The entire time period of study is divided into three phases, according to the intensity of vaccination drive. The impact of vaccination in controlling the spread of the pandemic is measured by studying the behavior of the coefficients of VAR model for these three time periods. Then, Granger causality is also measured. At 10% level of significance, it is found that if the number of infected is under-reported today, this is due to the significant influence of number of infected until previous two days. The number of discharged one day ago and three days ago also significantly influence this number. Number of tests conducted two days ago also significantly contributes to this underreporting. The impact of latent variables on the spread of COVID-19 is measured here.
{"title":"Vector Autoregression in Forecasting COVID-19 Under-Reporting–Nepal as a Case Study","authors":"Jyoti U. Devkota","doi":"10.3126/jnms.v5i2.50016","DOIUrl":"https://doi.org/10.3126/jnms.v5i2.50016","url":null,"abstract":"This paper aims to understand and predict the dynamics of spread of COVID-19. It is based on government data on COVID-19 from February 1, 2021 to August 31, 2021. First, Vector Autoregression (VAR) model is used here to model the interrelationships between time series data of daily tested, infected, dead and discharged. The impact of under-reporting on interrelated variables is quantified. The behavior of the parameters of these VAR model is also analyzed. The entire time period of study is divided into three phases, according to the intensity of vaccination drive. The impact of vaccination in controlling the spread of the pandemic is measured by studying the behavior of the coefficients of VAR model for these three time periods. Then, Granger causality is also measured. At 10% level of significance, it is found that if the number of infected is under-reported today, this is due to the significant influence of number of infected until previous two days. The number of discharged one day ago and three days ago also significantly influence this number. Number of tests conducted two days ago also significantly contributes to this underreporting. The impact of latent variables on the spread of COVID-19 is measured here.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130033820","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}
So far a large number of research works have been studied and investigated in basic sequence spaces c0, c, and l∞. In this present work, we introduce the difference sequence spaces W0(∆, f), W(∆, f) and W∞(∆, f) defined by non-negative real-valued Φ- function on R and study some of their topological properties defined by the paranormed structure on these spaces.
{"title":"On Certain Type of Difference Sequence Spaces Defined by Φ-Function","authors":"J. L. Ghimire, N. Pahari","doi":"10.3126/jnms.v5i2.50020","DOIUrl":"https://doi.org/10.3126/jnms.v5i2.50020","url":null,"abstract":"So far a large number of research works have been studied and investigated in basic sequence spaces c0, c, and l∞. In this present work, we introduce the difference sequence spaces W0(∆, f), W(∆, f) and W∞(∆, f) defined by non-negative real-valued Φ- function on R and study some of their topological properties defined by the paranormed structure on these spaces.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121529620","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 new application of positive and decreasing sequences to double Fourier series associated with (N, pm(1) ,pn(2)). Further, by considering some suitable conditions for previously known results, we have validated the current findings. This work is motivated by the works of [5] and [12].
{"title":"On a New Application of Positive and Decreasing Sequences to Double Fourier Series Associated with (N, p^(1)_m, p^(2)_n)","authors":"S. K. Sahani, G. Paudel, A. K. Thakur","doi":"10.3126/jnms.v5i2.50011","DOIUrl":"https://doi.org/10.3126/jnms.v5i2.50011","url":null,"abstract":"In this paper, we introduce a new application of positive and decreasing sequences to double Fourier series associated with (N, pm(1) ,pn(2)). Further, by considering some suitable conditions for previously known results, we have validated the current findings. This work is motivated by the works of [5] and [12].","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131916132","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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