Pub Date : 2020-12-01DOI: 10.4067/s0719-06462020000300325
B. Dhage
In this paper, we establish the existence and a global attractivity results for a nonlinear mixed quadratic and linearly perturbed hybrid fractional integrodifferential equation of second type involving the Caputo fractional derivative on unbounded intervals of real line with the mixed arguments of anticipations and retardation. The hybrid fixed point theorem of Dhage is used in the analysis of our nonlinear fractional integrodifferential problem. A positivity result is also obtained under certain usual natural conditions. Our hypotheses and claims have also been explained with the help of a natural realization.
{"title":"Existence and Attractivity Theorems for Nonlinear Hybrid Fractional Integrodifferential Equations with Anticipation and Retardation","authors":"B. Dhage","doi":"10.4067/s0719-06462020000300325","DOIUrl":"https://doi.org/10.4067/s0719-06462020000300325","url":null,"abstract":"In this paper, we establish the existence and a global attractivity results for a nonlinear mixed quadratic and linearly perturbed hybrid fractional integrodifferential equation of second type involving the Caputo fractional derivative on unbounded intervals of real line with the mixed arguments of anticipations and retardation. The hybrid fixed point theorem of Dhage is used in the analysis of our nonlinear fractional integrodifferential problem. A positivity result is also obtained under certain usual natural conditions. Our hypotheses and claims have also been explained with the help of a natural realization.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43977548","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 : 2020-08-27DOI: 10.4067/s0719-06462021000200239
Bruno Aguil'o Vidal
We give a simple construction for hyperelliptic varieties defined as the quotient of a complex torus by the action of a dihedral group that contains no translations and fixes no points. This generalizes a construction given by Catanese and Demleitner for $D_4$ in dimension three.
{"title":"Free dihedral actions on abelian varieties","authors":"Bruno Aguil'o Vidal","doi":"10.4067/s0719-06462021000200239","DOIUrl":"https://doi.org/10.4067/s0719-06462021000200239","url":null,"abstract":"We give a simple construction for hyperelliptic varieties defined as the quotient of a complex torus by the action of a dihedral group that contains no translations and fixes no points. This generalizes a construction given by Catanese and Demleitner for $D_4$ in dimension three.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42973939","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 : 2020-08-01DOI: 10.4067/s0719-06462020000200233
V. Govindan, Choonkill Park, S. Pinelas, T. Rassias
In this paper, we introduce the following ((a,b,c))-mixed type functional equation of the form (g(ax_1+bx_2+cx_3 )-g(-ax_1+bx_2+cx_3 ) + g(ax_1-bx_2+cx_3 ))(-g(ax_1+bx_2-cx_3 ) + 2a^2 [g(x_1 ) + g(-x_1)] + 2b^2 [g(x_2 ) + g(-x_2)] + )(2c^2 [g(x_3 ) + g(-x_3)]+a[g(x_1 ) - g(-x_1)]+ b[g(x_2 )-g(-x_2)] + ) (c[g(x_3 )-g(-x_3)]=4g(ax_1+cx_3 )+2g(-bx_2)+) (2g(bx_2)) where (a,b,c) are positive integers with (a>1), and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.
{"title":"Hyers-Ulam stability of an additive-quadratic functional equation","authors":"V. Govindan, Choonkill Park, S. Pinelas, T. Rassias","doi":"10.4067/s0719-06462020000200233","DOIUrl":"https://doi.org/10.4067/s0719-06462020000200233","url":null,"abstract":"In this paper, we introduce the following ((a,b,c))-mixed type functional equation of the form \u0000(g(ax_1+bx_2+cx_3 )-g(-ax_1+bx_2+cx_3 ) + g(ax_1-bx_2+cx_3 ))(-g(ax_1+bx_2-cx_3 ) + 2a^2 [g(x_1 ) + g(-x_1)] + 2b^2 [g(x_2 ) + g(-x_2)] + )(2c^2 [g(x_3 ) + g(-x_3)]+a[g(x_1 ) - g(-x_1)]+ b[g(x_2 )-g(-x_2)] + ) (c[g(x_3 )-g(-x_3)]=4g(ax_1+cx_3 )+2g(-bx_2)+) (2g(bx_2)) \u0000where (a,b,c) are positive integers with (a>1), and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46688821","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 : 2020-08-01DOI: 10.4067/s0719-06462020000200215
A. Kamal, T. I. Yassen
The aim of this paper is to introduce new hyperbolic classes of functions, which will be called ({mathcal{B}}^{*} _{alpha,;log}) and ({ F ^{*}_{log}}(p,q,s)) classes. Furthermore, we introduce (D)-metrics space in the hyperbolic type classes ({mathcal{B}}^{*} _{alpha,;log}) and ( { F ^{*}_{log}}(p,q,s)). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, necessary and sufficient conditions are given for the composition operator (C_phi) to be bounded and compact from ({mathcal{B}}^{*}_{alpha,;log}) to ({F ^{*}_{log}}(p,q,s)) spaces.
{"title":"D-metric Spaces and Composition Operators Between Hyperbolic Weighted Family of Function Spaces","authors":"A. Kamal, T. I. Yassen","doi":"10.4067/s0719-06462020000200215","DOIUrl":"https://doi.org/10.4067/s0719-06462020000200215","url":null,"abstract":"The aim of this paper is to introduce new hyperbolic classes of functions, which will be called ({mathcal{B}}^{*} _{alpha,;log}) and ({ F ^{*}_{log}}(p,q,s)) classes. Furthermore, we introduce (D)-metrics space in the hyperbolic type classes ({mathcal{B}}^{*} _{alpha,;log}) and ( { F ^{*}_{log}}(p,q,s)). These classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, necessary and sufficient conditions are given for the composition operator (C_phi) to be bounded and compact from ({mathcal{B}}^{*}_{alpha,;log}) to ({F ^{*}_{log}}(p,q,s)) spaces.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48254645","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 : 2020-08-01DOI: 10.4067/s0719-06462020000200177
R. Arora, Dharmendra Kumar, Ishita Jhamb, Avina Kaur Narang
Infection due to Chikungunya virus (CHIKV) has a substantially prolonged recuperation period that is a long period between the stage of infection and recovery. However, so far in the existing models (SIR and SEIR), this period has not been given due attention. Hence for this disease, we have modified the existing SEIR model by introducing a new section of human population which is in the recuperation stage or in other words the human population that is no more showing acute symptoms but is yet to attain complete recovery. A mathematical model is formulated and studied by means of existence and stability of its disease free equilibrium (DFE) and endemic equilibrium (EE) points in terms of the associated basic reproduction number ((R_0)).
{"title":"Mathematical Modeling of Chikungunya Dynamics: Stability and Simulation","authors":"R. Arora, Dharmendra Kumar, Ishita Jhamb, Avina Kaur Narang","doi":"10.4067/s0719-06462020000200177","DOIUrl":"https://doi.org/10.4067/s0719-06462020000200177","url":null,"abstract":"Infection due to Chikungunya virus (CHIKV) has a substantially prolonged recuperation period that is a long period between the stage of infection and recovery. However, so far in the existing models (SIR and SEIR), this period has not been given due attention. Hence for this disease, we have modified the existing SEIR model by introducing a new section of human population which is in the recuperation stage or in other words the human population that is no more showing acute symptoms but is yet to attain complete recovery. A mathematical model is formulated and studied by means of existence and stability of its disease free equilibrium (DFE) and endemic equilibrium (EE) points in terms of the associated basic reproduction number ((R_0)).","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44211417","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 : 2020-04-01DOI: 10.4067/s0719-06462020000100071
G. Divyashree, Venkatesha
The paper presents a study of ( (kappa,mu) )-contact metric manifolds satisfying certain conditions on the conharmonic curvature tensor.
本文研究了在共调和曲率张量上满足一定条件的接触度量流形。
{"title":"Certain results on the conharmonic curvature tensor of (κ, μ)-contact metric manifolds","authors":"G. Divyashree, Venkatesha","doi":"10.4067/s0719-06462020000100071","DOIUrl":"https://doi.org/10.4067/s0719-06462020000100071","url":null,"abstract":"The paper presents a study of ( (kappa,mu) )-contact metric manifolds satisfying certain conditions on the conharmonic curvature tensor.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43323614","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 : 2020-04-01DOI: 10.4067/s0719-06462020000100055
S. Nisha, P. K. Parida
In this paper, we have studied local convergence of Super-Halley method in Banach spaces under the assumption of second order majorant conditions. This approach allows us to obtain generalization of earlier convergence analysis under majorizing sequences. Two important special cases of the convergence analysis based on the premises of Kantorovich and Smale type conditions have also been concluded. To show efficacy of our approach we have given three numerical examples.
{"title":"Super-Halley method under majorant conditions in Banach spaces","authors":"S. Nisha, P. K. Parida","doi":"10.4067/s0719-06462020000100055","DOIUrl":"https://doi.org/10.4067/s0719-06462020000100055","url":null,"abstract":"In this paper, we have studied local convergence of Super-Halley method in Banach spaces under the assumption of second order majorant conditions. This approach allows us to obtain generalization of earlier convergence analysis under majorizing sequences. Two important special cases of the convergence analysis based on the premises of Kantorovich and Smale type conditions have also been concluded. To show efficacy of our approach we have given three numerical examples.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45332772","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 : 2020-04-01DOI: 10.4067/s0719-06462020000100125
D. Boucenna, A. B. Makhlouf, M. Hammami
In this paper, we investigate the existence and uniqueness of solutions for the Darboux problem of partial differential equations with Caputo-Katugampola fractional derivative.
{"title":"On Katugampola fractional order derivatives and Darboux problem for differential equations","authors":"D. Boucenna, A. B. Makhlouf, M. Hammami","doi":"10.4067/s0719-06462020000100125","DOIUrl":"https://doi.org/10.4067/s0719-06462020000100125","url":null,"abstract":"In this paper, we investigate the existence and uniqueness of solutions for the Darboux problem of partial differential equations with Caputo-Katugampola fractional derivative.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49007992","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 : 2020-04-01DOI: 10.4067/S0719-06462020000100001
S. Dragomir
In this paper we establish some bounds for the ( (Phi;f) )-mean difference introduced in the general settings of measurable spaces and Lebesgue integral, which is a two functions generalization of Gini mean difference that has been widely used by economists and sociologists to measure economic inequality.
{"title":"Bounds for the Generalized (Φ, f)-Mean Difference","authors":"S. Dragomir","doi":"10.4067/S0719-06462020000100001","DOIUrl":"https://doi.org/10.4067/S0719-06462020000100001","url":null,"abstract":"In this paper we establish some bounds for the ( (Phi;f) )-mean difference introduced in the general settings of measurable spaces and Lebesgue integral, which is a two functions generalization of Gini mean difference that has been widely used by economists and sociologists to measure economic inequality.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42880404","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 : 2020-04-01DOI: 10.4067/s0719-06462020000100137
M. Barro, S. Traoré
Given a coupling function (c) and a non empty subset of ℝ, we define a closure operator. We are interested in extended real-valued functions whose sub-level sets are closed for this operator. Since this class of functions is closed under pointwise suprema, we introduce a regularization for extended real-valued functions. By decomposition of the closure operator using polarity scheme, we recover the regularization by bi-conjugation. We apply our results to derive a strong duality for a minimization problem.
{"title":"Level sets regularization with application to optimization problems","authors":"M. Barro, S. Traoré","doi":"10.4067/s0719-06462020000100137","DOIUrl":"https://doi.org/10.4067/s0719-06462020000100137","url":null,"abstract":"Given a coupling function (c) and a non empty subset of ℝ, we define a closure operator. We are interested in extended real-valued functions whose sub-level sets are closed for this operator. Since this class of functions is closed under pointwise suprema, we introduce a regularization for extended real-valued functions. By decomposition of the closure operator using polarity scheme, we recover the regularization by bi-conjugation. We apply our results to derive a strong duality for a minimization problem.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47910077","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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