Pub Date : 2018-01-01DOI: 10.1080/23311835.2018.1428030
M. Khaleghi Moghadam, Lishan Liu
The existence of infinitely many solutions was investigated for an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary value condition. The technical approach is based on a local minimum theorem for differentiable functionals in finite dimensional space.
{"title":"Existence of infinitely many solutions for a class of difference equations with boundary value conditions involving p(k)-Laplacian operator","authors":"M. Khaleghi Moghadam, Lishan Liu","doi":"10.1080/23311835.2018.1428030","DOIUrl":"https://doi.org/10.1080/23311835.2018.1428030","url":null,"abstract":"The existence of infinitely many solutions was investigated for an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary value condition. The technical approach is based on a local minimum theorem for differentiable functionals in finite dimensional space.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1428030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60067338","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 : 2018-01-01DOI: 10.1080/23311835.2018.1446248
G. Aslam, M. Anwar
Abstract Hermite–Hadamard’s-type inequality is derived using superquadratic maps for positive operator semigroups. A methodical procedure was adopted to obtain the corresponding mean operators.
{"title":"Hermite–Hadamard’s inequality and Cauchy-type mean operators for positive -semigroups","authors":"G. Aslam, M. Anwar","doi":"10.1080/23311835.2018.1446248","DOIUrl":"https://doi.org/10.1080/23311835.2018.1446248","url":null,"abstract":"Abstract Hermite–Hadamard’s-type inequality is derived using superquadratic maps for positive operator semigroups. A methodical procedure was adopted to obtain the corresponding mean operators.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23311835.2018.1446248","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43040303","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 : 2018-01-01DOI: 10.1080/25742558.2018.1458933
W. Kumam, P. Sukprasert, P. Kumam, A. Shoaib, Aqeel Shahzad, Qasim Mahmood
In this paper, we establish some fixed point results for fuzzy mapping in a complete b-metric space. Our results unify, extend and generalize several results in the existing literature. Example is also given to support our results.
{"title":"Some fuzzy fixed point results for fuzzy mappings in complete b-metric spaces","authors":"W. Kumam, P. Sukprasert, P. Kumam, A. Shoaib, Aqeel Shahzad, Qasim Mahmood","doi":"10.1080/25742558.2018.1458933","DOIUrl":"https://doi.org/10.1080/25742558.2018.1458933","url":null,"abstract":"In this paper, we establish some fixed point results for fuzzy mapping in a complete b-metric space. Our results unify, extend and generalize several results in the existing literature. Example is also given to support our results.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1458933","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46864430","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 : 2018-01-01DOI: 10.1080/25742558.2018.1461530
C. Boonpok, C. Viriyapong
ABSTRACT This article deals with the notions of -open, -open, -open, -open, and -open sets. Several properties and the relationships between these concepts are discussed. Some characterizations of -extremally disconnected spaces and -hyperconnected spaces are investigated.
{"title":"On (Λ, θ)-open sets in topological spaces","authors":"C. Boonpok, C. Viriyapong","doi":"10.1080/25742558.2018.1461530","DOIUrl":"https://doi.org/10.1080/25742558.2018.1461530","url":null,"abstract":"ABSTRACT This article deals with the notions of -open, -open, -open, -open, and -open sets. Several properties and the relationships between these concepts are discussed. Some characterizations of -extremally disconnected spaces and -hyperconnected spaces are investigated.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1461530","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46081171","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 : 2018-01-01DOI: 10.1080/25742558.2018.1564531
Ousmane Koutou, B. Traoré, B. Sangaré
Abstract Generally, the infection process of most vector-borne diseases involves a latent period in both human hosts and vectors. With regards to other publications, Tian and Song have recently proposed an SIR-SI model to analyze the effects of the incubation period on a vector-borne disease with nonlinear transmission rate. But they were silent on the fact that the partially immune individuals are slightly infective to mosquitoes. So, by considering that the partially immune individuals remain slightly infective to mosquitoes, a similar work has been done in this paper for malaria global transmission dynamics following an SIRS-SI pattern. The basic reproduction ratio has been calculated using the next-generation matrix method. Furthermore, using the characteristic equations and inequality analytical techniques, conditions are given under which the system exhibits threshold behavior as follows: when R0 < 1, the disease-free equilibrium is globally asymptotically stable meaning that the disease will eventually die out; and the unique endemic equilibrium is globally asymptotically stable when R0 > 1 meaning that the disease will persist. Finally, some numerical simulations have been performed to illustrate our theoretical results.
{"title":"Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates","authors":"Ousmane Koutou, B. Traoré, B. Sangaré","doi":"10.1080/25742558.2018.1564531","DOIUrl":"https://doi.org/10.1080/25742558.2018.1564531","url":null,"abstract":"Abstract Generally, the infection process of most vector-borne diseases involves a latent period in both human hosts and vectors. With regards to other publications, Tian and Song have recently proposed an SIR-SI model to analyze the effects of the incubation period on a vector-borne disease with nonlinear transmission rate. But they were silent on the fact that the partially immune individuals are slightly infective to mosquitoes. So, by considering that the partially immune individuals remain slightly infective to mosquitoes, a similar work has been done in this paper for malaria global transmission dynamics following an SIRS-SI pattern. The basic reproduction ratio has been calculated using the next-generation matrix method. Furthermore, using the characteristic equations and inequality analytical techniques, conditions are given under which the system exhibits threshold behavior as follows: when R0 < 1, the disease-free equilibrium is globally asymptotically stable meaning that the disease will eventually die out; and the unique endemic equilibrium is globally asymptotically stable when R0 > 1 meaning that the disease will persist. Finally, some numerical simulations have been performed to illustrate our theoretical results.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1564531","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41651567","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 : 2018-01-01DOI: 10.1080/25742558.2018.1463597
Saida Bendaas
In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis.
{"title":"Periodic wave shock solutions of Burgers equations","authors":"Saida Bendaas","doi":"10.1080/25742558.2018.1463597","DOIUrl":"https://doi.org/10.1080/25742558.2018.1463597","url":null,"abstract":"In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1463597","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48683682","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 : 2018-01-01DOI: 10.1080/25742558.2018.1460030
M. El-Borai, K. El-Nadi, H. Ahmed, H. El-Owaidy, A. Ghanem, R. Sakthivel
In this paper, a nonlinear fractional parabolic stochastic integro-partial differential equations with nonlocal effects driven by a fractional Brownian motion is considered. In particular, first we have formulated the suitable solution form for the fractional partial differential equations with nonlocal effects driven by fractional Brownian motion using a parabolic transform. Next, the existence and uniqueness of solutions are obtained for the fractional stochastic partial differential equations without any restrictions on the characteristic forms when the Hurst parameter of the fractional Brownian motion is less than half. Further, we investigate the stability of the solution for the considered problem. The required result is established by means of standard Picard’s iteration.
{"title":"Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition","authors":"M. El-Borai, K. El-Nadi, H. Ahmed, H. El-Owaidy, A. Ghanem, R. Sakthivel","doi":"10.1080/25742558.2018.1460030","DOIUrl":"https://doi.org/10.1080/25742558.2018.1460030","url":null,"abstract":"In this paper, a nonlinear fractional parabolic stochastic integro-partial differential equations with nonlocal effects driven by a fractional Brownian motion is considered. In particular, first we have formulated the suitable solution form for the fractional partial differential equations with nonlocal effects driven by fractional Brownian motion using a parabolic transform. Next, the existence and uniqueness of solutions are obtained for the fractional stochastic partial differential equations without any restrictions on the characteristic forms when the Hurst parameter of the fractional Brownian motion is less than half. Further, we investigate the stability of the solution for the considered problem. The required result is established by means of standard Picard’s iteration.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1460030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42840874","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 : 2018-01-01DOI: 10.1080/25742558.2018.1458555
Deniz Ilalan, Özgür Özel
Abstract We consider arctangent as the logistic function and compute the asymptotic critical values of the related non-linear unit root test via Monte Carlo simulation. While doing so, we got inspiration from some pioneering articles and use first-order Taylor approximation. We observe that this newly proposed test exhibits higher power than some well-known linear and non-linear tests. We apply our test to some stock indexes and find out that a non-linear arctangent trend can be at stage, rather than a linear unit root process.
{"title":"Non-linear unit root testing with arctangent trend: Simulation and applications in finance","authors":"Deniz Ilalan, Özgür Özel","doi":"10.1080/25742558.2018.1458555","DOIUrl":"https://doi.org/10.1080/25742558.2018.1458555","url":null,"abstract":"Abstract We consider arctangent as the logistic function and compute the asymptotic critical values of the related non-linear unit root test via Monte Carlo simulation. While doing so, we got inspiration from some pioneering articles and use first-order Taylor approximation. We observe that this newly proposed test exhibits higher power than some well-known linear and non-linear tests. We apply our test to some stock indexes and find out that a non-linear arctangent trend can be at stage, rather than a linear unit root process.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1458555","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45953658","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 : 2018-01-01DOI: 10.1080/25742558.2018.1473709
Serbun Ufuk Değer, Y. Bolat
Abstract In this paper, we give some new necessary and sufficient conditions for the asymptotic stability of a class of time–delay systems of the form where is a real number, is a real constant matrix, and , are positive numbers such that .
摘要本文给出了一类时滞系统渐近稳定的几个新的充要条件，其中是实数，是实常数矩阵，是正数，使得。
{"title":"On asymptotic stability of a class of time–delay systems","authors":"Serbun Ufuk Değer, Y. Bolat","doi":"10.1080/25742558.2018.1473709","DOIUrl":"https://doi.org/10.1080/25742558.2018.1473709","url":null,"abstract":"Abstract In this paper, we give some new necessary and sufficient conditions for the asymptotic stability of a class of time–delay systems of the form where is a real number, is a real constant matrix, and , are positive numbers such that .","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1473709","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43777434","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 : 2018-01-01DOI: 10.1080/25742558.2018.1464880
Y. Khalili, A. Neamaty
Abstract In this article, we present some results about the Sturm–Liouville equation with turning points and singularities and transform them to each other. By applying a change of a variable, we can transform the differential equation with a turning point to the differential equation with a singularity. Also we will prove that a differential equation with a singularity will be transformed to a differential equation with a turning point in some cases.
{"title":"On the relationship between the turning and singular points in Sturm–Liouville equations","authors":"Y. Khalili, A. Neamaty","doi":"10.1080/25742558.2018.1464880","DOIUrl":"https://doi.org/10.1080/25742558.2018.1464880","url":null,"abstract":"Abstract In this article, we present some results about the Sturm–Liouville equation with turning points and singularities and transform them to each other. By applying a change of a variable, we can transform the differential equation with a turning point to the differential equation with a singularity. Also we will prove that a differential equation with a singularity will be transformed to a differential equation with a turning point in some cases.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1464880","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45892220","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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