Pub Date : 2015-12-01DOI: 10.1515/AUPCSM-2015-0007
Z. Moszner
Abstract We consider the stability, the superstability and the inverse stability of the functional equations with squares of Cauchy’s, of Jensen’s and of isometry equations and the stability in Ulam-Hyers sense of the alternation of functional equations and of the equation of isometry.
{"title":"On the stability of the squares of some functional equations","authors":"Z. Moszner","doi":"10.1515/AUPCSM-2015-0007","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0007","url":null,"abstract":"Abstract We consider the stability, the superstability and the inverse stability of the functional equations with squares of Cauchy’s, of Jensen’s and of isometry equations and the stability in Ulam-Hyers sense of the alternation of functional equations and of the equation of isometry.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"43 1","pages":"81 - 104"},"PeriodicalIF":0.9,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76235184","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 : 2015-11-30DOI: 10.1515/AUPCSM-2015-0010
S. Datta, T. Biswas, Ahsanul Hoque
Abstract In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.
{"title":"Comparative growth analysis of Wronskians in the light of their relative orders","authors":"S. Datta, T. Biswas, Ahsanul Hoque","doi":"10.1515/AUPCSM-2015-0010","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0010","url":null,"abstract":"Abstract In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"105 1","pages":"135 - 148"},"PeriodicalIF":0.9,"publicationDate":"2015-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86963877","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 : 2015-09-23DOI: 10.1515/aupcsm-2015-0008
A. Banerjee, B. Chakraborty
Abstract In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
{"title":"Further investigations on a question of Zhang and Lü","authors":"A. Banerjee, B. Chakraborty","doi":"10.1515/aupcsm-2015-0008","DOIUrl":"https://doi.org/10.1515/aupcsm-2015-0008","url":null,"abstract":"Abstract In the paper based on the question of Zhang and Lü [15], we present one theorem which will improve and extend results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"42 1","pages":"105 - 119"},"PeriodicalIF":0.9,"publicationDate":"2015-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75621225","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 : 2015-04-28DOI: 10.1515/AUPCSM-2015-0004
L. Klimczak
Abstract We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.
{"title":"Two constant sign solutions for a nonhomogeneous Neumann boundary value problem","authors":"L. Klimczak","doi":"10.1515/AUPCSM-2015-0004","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0004","url":null,"abstract":"Abstract We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"38 1","pages":"47 - 62"},"PeriodicalIF":0.9,"publicationDate":"2015-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82603211","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 : 2015-03-16DOI: 10.2478/aupcsm-2018-0003
G. Murugusundaramoorthy, T. Bulboacă
Abstract In this paper, we define a new subclass of bi-univalent functions involving a Hohlov operator in the open unit disk. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.
{"title":"Estimate for initial MacLaurin coefficients of certain subclasses of bi-univalent functions of complex order associated with the Hohlov operator","authors":"G. Murugusundaramoorthy, T. Bulboacă","doi":"10.2478/aupcsm-2018-0003","DOIUrl":"https://doi.org/10.2478/aupcsm-2018-0003","url":null,"abstract":"Abstract In this paper, we define a new subclass of bi-univalent functions involving a Hohlov operator in the open unit disk. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"20 1","pages":"27 - 36"},"PeriodicalIF":0.9,"publicationDate":"2015-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81952870","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 : 2015-02-20DOI: 10.1515/AUPCSM-2015-0003
Jakub Szotek
Abstract In the paper we give a mathematical overview of the CreditRisk+ model as a tool used for calculating credit risk in a portfolio of debts and suggest some other applications of the same method of analysis.
{"title":"Generalized CreditRisk+ model and applications","authors":"Jakub Szotek","doi":"10.1515/AUPCSM-2015-0003","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0003","url":null,"abstract":"Abstract In the paper we give a mathematical overview of the CreditRisk+ model as a tool used for calculating credit risk in a portfolio of debts and suggest some other applications of the same method of analysis.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"128 1","pages":"37 - 46"},"PeriodicalIF":0.9,"publicationDate":"2015-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89198961","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 : 2015-01-13DOI: 10.1515/AUPCSM-2015-0002
L. Skóra
Abstract We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.
摘要给出了一类具有不动点脉冲的二阶泛函微分方程边值问题的存在唯一性结果。
{"title":"Boundary value problem for the second order impulsive delay differential equations","authors":"L. Skóra","doi":"10.1515/AUPCSM-2015-0002","DOIUrl":"https://doi.org/10.1515/AUPCSM-2015-0002","url":null,"abstract":"Abstract We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"46 1","pages":"27 - 35"},"PeriodicalIF":0.9,"publicationDate":"2015-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74238351","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 : 2014-12-01DOI: 10.2478/AUPCSM-2014-0002
K. Kliś-Garlicka
Abstract It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.
摘要证明了被有限秩算子扰动的Toeplitz算子空间是2-超自反的。
{"title":"Perturbation of Toeplitz operators and reflexivity","authors":"K. Kliś-Garlicka","doi":"10.2478/AUPCSM-2014-0002","DOIUrl":"https://doi.org/10.2478/AUPCSM-2014-0002","url":null,"abstract":"Abstract It was shown that the space of Toeplitz operators perturbated by finite rank operators is 2-hyperreflexive.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"18 1","pages":"15 - 18"},"PeriodicalIF":0.9,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78928628","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 : 2014-12-01DOI: 10.2478/AUPCSM-2014-0004
Monika Herzog
Abstract In this paper we study approximation properties of partial modified Szasz-Mirakyan operators for functions from exponential weight spaces. We present some direct theorems giving the degree of approximation for these operators. The considered version of Szász-Mirakyan operators is more useful from the computational point of view.
{"title":"A note on the convergence of partial Szász-Mirakyan type operators","authors":"Monika Herzog","doi":"10.2478/AUPCSM-2014-0004","DOIUrl":"https://doi.org/10.2478/AUPCSM-2014-0004","url":null,"abstract":"Abstract In this paper we study approximation properties of partial modified Szasz-Mirakyan operators for functions from exponential weight spaces. We present some direct theorems giving the degree of approximation for these operators. The considered version of Szász-Mirakyan operators is more useful from the computational point of view.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"10 1","pages":"45 - 50"},"PeriodicalIF":0.9,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84614172","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 : 2014-12-01DOI: 10.2478/AUPCSM-2014-0003
Maria Robaszewska
Abstract For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0. This work was intended as an attempt to describe in a unified way the construction of similar 1-forms known for constant Gauss curvature surfaces, in particular of that given by R. Sasaki for pseudospherical surfaces.
{"title":"On some flat connection associated with locally symmetric surface","authors":"Maria Robaszewska","doi":"10.2478/AUPCSM-2014-0003","DOIUrl":"https://doi.org/10.2478/AUPCSM-2014-0003","url":null,"abstract":"Abstract For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0. This work was intended as an attempt to describe in a unified way the construction of similar 1-forms known for constant Gauss curvature surfaces, in particular of that given by R. Sasaki for pseudospherical surfaces.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"7 1","pages":"19 - 43"},"PeriodicalIF":0.9,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79065436","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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