Pub Date : 2018-12-31DOI: 10.30538/psrp-oma2018.0016
Dhruba R. Adhikar, Ishwari J. Kunwar
Let D be an open subset of RN and f : D → RN a continuous function. The classical topological degree for f demands that D be bounded. The boundedness of domains is also assumed for the topological degrees for compact displacements of the identity and for operators of monotone type in Banach spaces. In this work, we follow the methodology introduced by Nagumo for constructing topological degrees for functions on unbounded domains in finite dimensions and define the degrees for LeraySchauder operators and (S+)-operators on unbounded domains in infinite dimensions. Mathematics Subject Classification: Primary 47H14; Secondary 47H05, 47H11.
{"title":"Topological Degrees on Unbounded Domains","authors":"Dhruba R. Adhikar, Ishwari J. Kunwar","doi":"10.30538/psrp-oma2018.0016","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0016","url":null,"abstract":"Let D be an open subset of RN and f : D → RN a continuous function. The classical topological degree for f demands that D be bounded. The boundedness of domains is also assumed for the topological degrees for compact displacements of the identity and for operators of monotone type in Banach spaces. In this work, we follow the methodology introduced by Nagumo for constructing topological degrees for functions on unbounded domains in finite dimensions and define the degrees for LeraySchauder operators and (S+)-operators on unbounded domains in infinite dimensions. Mathematics Subject Classification: Primary 47H14; Secondary 47H05, 47H11.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46070151","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 : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0018
L. Rachdi, S. Sghaier
{"title":"Lp− Boundedness for Integral Transforms Associated with Singular Partial Differential Operators","authors":"L. Rachdi, S. Sghaier","doi":"10.30538/PSRP-OMA2018.0018","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0018","url":null,"abstract":"","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41747045","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 : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0022
H. Darwish, S. Sowileh, A. Y. Lashin
Let A be the class of analytic and univalent functions in the open unit disc ∆ normalized such that f(0) = 0 = f ′(0)− 1. In this paper, for ψ ∈ A of the form z f(z) , f(z) = 1 + ∞ ∑ n=1 anz n and 0 ≤ α ≤ 1, we introduce and investigate interesting subclasses Hσ(φ), Sσ(α, φ), Mσ(α, φ), =α(α, φ) and βα(λ, φ) (λ ≥ 0) of analytic and bi-univalent Ma-Minda starlike and convex functions. Furthermore, we find estimates on the coefficients |a1| and |a2| for functions in these classess. Several related classes of functions are also considered. Mathematics Subject Classification: 30C45.
{"title":"Coefficient Estimates of some Classes of Rational Functions","authors":"H. Darwish, S. Sowileh, A. Y. Lashin","doi":"10.30538/PSRP-OMA2018.0022","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0022","url":null,"abstract":"Let A be the class of analytic and univalent functions in the open unit disc ∆ normalized such that f(0) = 0 = f ′(0)− 1. In this paper, for ψ ∈ A of the form z f(z) , f(z) = 1 + ∞ ∑ n=1 anz n and 0 ≤ α ≤ 1, we introduce and investigate interesting subclasses Hσ(φ), Sσ(α, φ), Mσ(α, φ), =α(α, φ) and βα(λ, φ) (λ ≥ 0) of analytic and bi-univalent Ma-Minda starlike and convex functions. Furthermore, we find estimates on the coefficients |a1| and |a2| for functions in these classess. Several related classes of functions are also considered. Mathematics Subject Classification: 30C45.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41422718","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 : 2018-12-31DOI: 10.30538/psrp-oma2018.0026
Sabir Yasin, Amir Naseem
In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method. Mathematics Subject Classification: 37F50.
{"title":"Higher Order Nonlinear Equation Solvers and their Dynamical Behavior","authors":"Sabir Yasin, Amir Naseem","doi":"10.30538/psrp-oma2018.0026","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0026","url":null,"abstract":"In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method. Mathematics Subject Classification: 37F50.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48395135","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 : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0025
C. Raposo, A. Cattai, J. Ribeiro
In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation utt − ∆pu = ∆u− g ∗ ∆u where ∆pu is the nonlinear p-Laplacian operator, p ≥ 2 and g ∗ ∆u is a memory damping. The global solution is constructed by means of the Faedo-Galerkin approximations taking into account that the initial data is in appropriated set of stability created from the Nehari manifold and the asymptotic behavior is obtained by using a result of P. Martinez based on new inequality that generalizes the results of Haraux and Nakao. Mathematics Subject Classification: 35B40, 35L70, 35A01, 74DXX.
{"title":"Global Solution and Asymptotic Behaviour for a Wave Equation type p-Laplacian with Memory","authors":"C. Raposo, A. Cattai, J. Ribeiro","doi":"10.30538/PSRP-OMA2018.0025","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0025","url":null,"abstract":"In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation utt − ∆pu = ∆u− g ∗ ∆u where ∆pu is the nonlinear p-Laplacian operator, p ≥ 2 and g ∗ ∆u is a memory damping. The global solution is constructed by means of the Faedo-Galerkin approximations taking into account that the initial data is in appropriated set of stability created from the Nehari manifold and the asymptotic behavior is obtained by using a result of P. Martinez based on new inequality that generalizes the results of Haraux and Nakao. Mathematics Subject Classification: 35B40, 35L70, 35A01, 74DXX.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48789451","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 : 2018-12-31DOI: 10.30538/psrp-oma2018.0021
Jian Dang, Qingying Hu, Hongwei Zhang
In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish both the existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow-up result for solutions with positive and negative initial energy respectively. Mathematics Subject Classification: 35K05; 35K61; 35K70.
{"title":"Asymptotic Stability and Blow-up of Solutions for the Generalized Boussinesq Equation with Nonlinear Boundary Condition","authors":"Jian Dang, Qingying Hu, Hongwei Zhang","doi":"10.30538/psrp-oma2018.0021","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0021","url":null,"abstract":"In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish both the existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow-up result for solutions with positive and negative initial energy respectively. Mathematics Subject Classification: 35K05; 35K61; 35K70.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46642777","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 : 2018-12-31DOI: 10.30538/psrp-oma2018.0023
S. Harikrishnan, E. Elsayed, K. Kanagarajan
In this paper, we find a solution of a new type of Langevin equation involving Hilfer fractional derivatives with impulsive effect. We formulate sufficient conditions for the existence and uniqueness of solutions. Moreover, we present Hyers-Ulam stability results. Mathematics Subject Classification: 26A33, 34K40, 34K14.
{"title":"Analytic Study on Hilfer Fractional Langevin Equations with Impulses","authors":"S. Harikrishnan, E. Elsayed, K. Kanagarajan","doi":"10.30538/psrp-oma2018.0023","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0023","url":null,"abstract":"In this paper, we find a solution of a new type of Langevin equation involving Hilfer fractional derivatives with impulsive effect. We formulate sufficient conditions for the existence and uniqueness of solutions. Moreover, we present Hyers-Ulam stability results. Mathematics Subject Classification: 26A33, 34K40, 34K14.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46280246","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 : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0020
A. Ramm
It is proved that if the problem ∇2u = 1 in D, u|S = 0, uN = m := |D|/|S| then D is a ball. There were at least two different proofs published of this result. The proof given in this paper is novel and short. Mathematics Subject Classification: 35B06; 35R30; 35J05.
{"title":"Old Symmetry Problem Revisited","authors":"A. Ramm","doi":"10.30538/PSRP-OMA2018.0020","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0020","url":null,"abstract":"It is proved that if the problem ∇2u = 1 in D, u|S = 0, uN = m := |D|/|S| then D is a ball. There were at least two different proofs published of this result. The proof given in this paper is novel and short. Mathematics Subject Classification: 35B06; 35R30; 35J05.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47798251","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 : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0017
A. Ramm
Let S be a C1-smooth closed connected surface in R3, the boundary of the domain D, N = Ns be the unit outer normal to S at the point s, P be the normal section of D. A normal section is the intersection of D and the plane containing N . It is proved that if all the normal sections for a fixed N are discs, then S is a sphere. The converse statement is trivial. Mathematics Subject Classification: 53A05.
{"title":"Necessary and Sufficient Condition for a Surface to be a Sphere","authors":"A. Ramm","doi":"10.30538/PSRP-OMA2018.0017","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0017","url":null,"abstract":"Let S be a C1-smooth closed connected surface in R3, the boundary of the domain D, N = Ns be the unit outer normal to S at the point s, P be the normal section of D. A normal section is the intersection of D and the plane containing N . It is proved that if all the normal sections for a fixed N are discs, then S is a sphere. The converse statement is trivial. Mathematics Subject Classification: 53A05.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45768979","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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