Pub Date : 2016-12-01DOI: 10.1515/AUPCSM-2016-0003
Damian Wiśniewski, Mariusz Bodzioch
Abstract We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
{"title":"An integro-differential inequality related to the smallest positive eigenvalue of p(x)-Laplacian Dirichlet problem","authors":"Damian Wiśniewski, Mariusz Bodzioch","doi":"10.1515/AUPCSM-2016-0003","DOIUrl":"https://doi.org/10.1515/AUPCSM-2016-0003","url":null,"abstract":"Abstract We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"30 1","pages":"27 - 36"},"PeriodicalIF":0.9,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83332436","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 : 2016-11-29DOI: 10.1515/AUPCSM-2016-0010
F. Lehlou, M. Moussa, A. Roukbi, S. Kabbaj
Abstract In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(xsigma (y)a) + f(xya) = 2f(x)f(y)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f(xsigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.
{"title":"On the superstability of the cosine and sine type functional equations","authors":"F. Lehlou, M. Moussa, A. Roukbi, S. Kabbaj","doi":"10.1515/AUPCSM-2016-0010","DOIUrl":"https://doi.org/10.1515/AUPCSM-2016-0010","url":null,"abstract":"Abstract In this paper, we study the superstablity problem of the cosine and sine type functional equations: f(xσ(y)a)+f(xya)=2f(x)f(y) $$f(xsigma (y)a) + f(xya) = 2f(x)f(y)$$ and f(xσ(y)a)−f(xya)=2f(x)f(y), $$f(xsigma (y)a) - f(xya) = 2f(x)f(y),$$ where f : S → ℂ is a complex valued function; S is a semigroup; σ is an involution of S and a is a fixed element in the center of S.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"44 1","pages":"113 - 121"},"PeriodicalIF":0.9,"publicationDate":"2016-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73671823","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 : 2016-11-21DOI: 10.1515/AUPCSM-2016-0009
K. Rajchel, J. Szczȩsny
Abstract A new method to solve stationary one-dimensional Schroedinger equation is investigated. Solutions are described by means of representation of circles with multiple winding number. The results are demonstrated using the well-known analytical solutions of the Schroedinger equation.
{"title":"New method to solve certain differential equations","authors":"K. Rajchel, J. Szczȩsny","doi":"10.1515/AUPCSM-2016-0009","DOIUrl":"https://doi.org/10.1515/AUPCSM-2016-0009","url":null,"abstract":"Abstract A new method to solve stationary one-dimensional Schroedinger equation is investigated. Solutions are described by means of representation of circles with multiple winding number. The results are demonstrated using the well-known analytical solutions of the Schroedinger equation.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"48 1","pages":"107 - 111"},"PeriodicalIF":0.9,"publicationDate":"2016-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85890101","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 : 2016-11-09DOI: 10.1515/AUPCSM-2016-0007
M. A. A. Khan
Abstract In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.
{"title":"Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces","authors":"M. A. A. Khan","doi":"10.1515/AUPCSM-2016-0007","DOIUrl":"https://doi.org/10.1515/AUPCSM-2016-0007","url":null,"abstract":"Abstract In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"35 1","pages":"79 - 96"},"PeriodicalIF":0.9,"publicationDate":"2016-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75038194","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 : 2016-04-22DOI: 10.1515/AUPCSM-2016-0002
A. Walendziak
Abstract In this paper we define strong ideals and horizontal ideals in pseudo-BCH-algebras and investigate the properties and characterizations of them.
摘要本文定义了伪bch -代数中的强理想和水平理想，并研究了它们的性质和刻画。
{"title":"Strong ideals and horizontal ideals in pseudo-BCH-algebras","authors":"A. Walendziak","doi":"10.1515/AUPCSM-2016-0002","DOIUrl":"https://doi.org/10.1515/AUPCSM-2016-0002","url":null,"abstract":"Abstract In this paper we define strong ideals and horizontal ideals in pseudo-BCH-algebras and investigate the properties and characterizations of them.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"6 1","pages":"15 - 25"},"PeriodicalIF":0.9,"publicationDate":"2016-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75404462","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 : 2016-01-17DOI: 10.1515/AUPCSM-2016-0001
Iz-iddine El-Fassi
Abstract The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) $$f(x + y + z) + f(x + y + sigma (z)) + f(x + sigma (y) + z) + f(sigma (x) + y + z) = 4f(x)f(y)f(z)$$ for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.
摘要本文研究了d 'Alembert型泛函方程f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) $$f(x + y + z) + f(x + y + sigma (z)) + f(x + sigma (y) + z) + f(sigma (x) + y + z) = 4f(x)f(y)f(z)$$对于所有x, y, z∈G，其中G是一个阿贝尔群，σ: G→G是一个自同态，使得σ(σ(x)) = x对于未知函数f从G转化为或转化为可交换半单Banach代数。
{"title":"On the superstability of generalized d’Alembert harmonic functions","authors":"Iz-iddine El-Fassi","doi":"10.1515/AUPCSM-2016-0001","DOIUrl":"https://doi.org/10.1515/AUPCSM-2016-0001","url":null,"abstract":"Abstract The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) $$f(x + y + z) + f(x + y + sigma (z)) + f(x + sigma (y) + z) + f(sigma (x) + y + z) = 4f(x)f(y)f(z)$$ for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"14 1","pages":"5 - 13"},"PeriodicalIF":0.9,"publicationDate":"2016-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75452912","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 : 2015-12-01DOI: 10.1515/AUPCSM-2015-0005
M. Skrzyński
Abstract Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).
{"title":"A note on preserving the spark of a matrix","authors":"M. Skrzyński","doi":"10.1515/AUPCSM-2015-0005","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0005","url":null,"abstract":"Abstract Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"12 1","pages":"63 - 67"},"PeriodicalIF":0.9,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78756910","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 : 2015-12-01DOI: 10.1515/AUPCSM-2015-0006
Renata Malejki
Abstract We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.
{"title":"Stability of a generalization of the Fréchet functional equation","authors":"Renata Malejki","doi":"10.1515/AUPCSM-2015-0006","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0006","url":null,"abstract":"Abstract We prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"46 1","pages":"69 - 79"},"PeriodicalIF":0.9,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88488064","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 : 2015-12-01DOI: 10.1515/AUPCSM-2015-0001
M. Ślosarski
Abstract In this paper a new class of multi-valued mappings (multi-morphisms) is defined as a version of a strongly admissible mapping, and its properties and applications are presented.
摘要本文定义了一类新的多值映射(多态)，它是强允许映射的一个版本，并给出了它的性质和应用。
{"title":"The multi-morphisms and their properties and applications","authors":"M. Ślosarski","doi":"10.1515/AUPCSM-2015-0001","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0001","url":null,"abstract":"Abstract In this paper a new class of multi-valued mappings (multi-morphisms) is defined as a version of a strongly admissible mapping, and its properties and applications are presented.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"44 1","pages":"5 - 25"},"PeriodicalIF":0.9,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87449059","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 : 2015-12-01DOI: 10.1515/AUPCSM-2015-0011
Y. Aribou, H. Dimou, A. Chahbi, S. Kabbaj
Abstract In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation where E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation.
{"title":"Stability of generalized quadratic functional equation on a set of measure zero","authors":"Y. Aribou, H. Dimou, A. Chahbi, S. Kabbaj","doi":"10.1515/AUPCSM-2015-0011","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0011","url":null,"abstract":"Abstract In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation where E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"11 1","pages":"149 - 162"},"PeriodicalIF":0.9,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79736526","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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