Pub Date : 2018-12-01DOI: 10.2478/aupcsm-2018-0007
A. Lau, Y. Zhang
Abstract It has been a long-standing problem posed by the first author in a conference in Marseille in 1990 to characterize semitopological semigroups which have common fixed point property when acting on a nonempty weak* compact convex subset of a dual Banach space as weak* continuous and norm nonexpansive mappings. Our investigation in the paper centers around this problem. Our main results rely on the well-known Ky Fan’s inequality for convex functions.
{"title":"Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces","authors":"A. Lau, Y. Zhang","doi":"10.2478/aupcsm-2018-0007","DOIUrl":"https://doi.org/10.2478/aupcsm-2018-0007","url":null,"abstract":"Abstract It has been a long-standing problem posed by the first author in a conference in Marseille in 1990 to characterize semitopological semigroups which have common fixed point property when acting on a nonempty weak* compact convex subset of a dual Banach space as weak* continuous and norm nonexpansive mappings. Our investigation in the paper centers around this problem. Our main results rely on the well-known Ky Fan’s inequality for convex functions.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"14 1","pages":"67 - 87"},"PeriodicalIF":0.9,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81931212","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 : 2018-12-01DOI: 10.2478/aupcsm-2018-0005
K. Gryszka
Abstract We study three properties associated to the recurrence of orbits in flows: asymptotic periodicity, positive asymptotic periodicity and G-asymptotic periodicity. We determine which implications between these notions hold and which do not. We also show how these notions are related to Lyapunov stability.
{"title":"On asymptotically periodic-like motions in flows","authors":"K. Gryszka","doi":"10.2478/aupcsm-2018-0005","DOIUrl":"https://doi.org/10.2478/aupcsm-2018-0005","url":null,"abstract":"Abstract We study three properties associated to the recurrence of orbits in flows: asymptotic periodicity, positive asymptotic periodicity and G-asymptotic periodicity. We determine which implications between these notions hold and which do not. We also show how these notions are related to Lyapunov stability.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"5 1","pages":"45 - 57"},"PeriodicalIF":0.9,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73206213","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 : 2018-12-01DOI: 10.2478/aupcsm-2018-0001
G. Murugusundaramoorthy, S. Bulut
Abstract In this paper, we define a new subclass of bi-univalent functions involving q-difference 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":"Bi-Bazilevič functions of complex order involving Ruscheweyh type q-difference operator","authors":"G. Murugusundaramoorthy, S. Bulut","doi":"10.2478/aupcsm-2018-0001","DOIUrl":"https://doi.org/10.2478/aupcsm-2018-0001","url":null,"abstract":"Abstract In this paper, we define a new subclass of bi-univalent functions involving q-difference 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":"102 1","pages":"15 - 5"},"PeriodicalIF":0.9,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89152436","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 : 2018-07-11DOI: 10.2478/aupcsm-2018-0006
Hassan Haghighi, M. Mosakhani, Mohammad Zaman Fashami
Abstract Let Zn = p0 + p1 + ··· + pn be a configuration of points in ℙ2, where all points pi except p0 lie on a line, and let I(Zn) be its corresponding homogeneous ideal in 𝕂 [ℙ2]. The resurgence and the Waldschmidt constant of I(Zn) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme Zn,c = cp0 + p1 +··· + pn, i.e. the point p0 is considered with multiplicity c. Our strategy is similar to [5].
{"title":"Resurgence and Waldschmidt constant of the ideal of a fat almost collinear subscheme in ℙ2","authors":"Hassan Haghighi, M. Mosakhani, Mohammad Zaman Fashami","doi":"10.2478/aupcsm-2018-0006","DOIUrl":"https://doi.org/10.2478/aupcsm-2018-0006","url":null,"abstract":"Abstract Let Zn = p0 + p1 + ··· + pn be a configuration of points in ℙ2, where all points pi except p0 lie on a line, and let I(Zn) be its corresponding homogeneous ideal in 𝕂 [ℙ2]. The resurgence and the Waldschmidt constant of I(Zn) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme Zn,c = cp0 + p1 +··· + pn, i.e. the point p0 is considered with multiplicity c. Our strategy is similar to [5].","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"53 1","pages":"59 - 65"},"PeriodicalIF":0.9,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84762685","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 : 2018-04-10DOI: 10.2478/aupcsm-2020-0002
P. Pasteczka
We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary. It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.
{"title":"Jensen-type geometric shapes","authors":"P. Pasteczka","doi":"10.2478/aupcsm-2020-0002","DOIUrl":"https://doi.org/10.2478/aupcsm-2020-0002","url":null,"abstract":"\u0000 We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.\u0000 It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"7 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89782487","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 : 2017-12-03DOI: 10.2478/aupcsm-2018-0002
M. Rossafi, Samir Kabbaj
Abstract In this paper, we study ∗-g-frames in tensor products of Hilbert C∗-modules. We show that a tensor product of two ∗-g-frames is a ∗-g-frame, and we get some result.
摘要本文研究Hilbert C * -模张量积中的* -g坐标系。证明了两个* -g坐标系的张量积是一个* -g坐标系，并得到了一些结果。
{"title":"*-g-frames in tensor products of Hilbert C*-modules","authors":"M. Rossafi, Samir Kabbaj","doi":"10.2478/aupcsm-2018-0002","DOIUrl":"https://doi.org/10.2478/aupcsm-2018-0002","url":null,"abstract":"Abstract In this paper, we study ∗-g-frames in tensor products of Hilbert C∗-modules. We show that a tensor product of two ∗-g-frames is a ∗-g-frame, and we get some result.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"13 1","pages":"17 - 25"},"PeriodicalIF":0.9,"publicationDate":"2017-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74004040","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 : 2017-12-01DOI: 10.1515/aupcsm-2017-0007
Sk. Nazmul
Abstract In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short) and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.
{"title":"On type-2 m-topological spaces","authors":"Sk. Nazmul","doi":"10.1515/aupcsm-2017-0007","DOIUrl":"https://doi.org/10.1515/aupcsm-2017-0007","url":null,"abstract":"Abstract In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short) and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"3 1","pages":"77 - 93"},"PeriodicalIF":0.9,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88766625","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 : 2017-12-01DOI: 10.1515/aupcsm-2017-0009
Z. Moszner
Abstract A connection between the continuous translation equation and the Jordan non-measurable continuous functions is given.
摘要给出了连续平移方程与Jordan不可测连续函数之间的联系。
{"title":"Translation equation and the Jordan non-measurable continuous functions","authors":"Z. Moszner","doi":"10.1515/aupcsm-2017-0009","DOIUrl":"https://doi.org/10.1515/aupcsm-2017-0009","url":null,"abstract":"Abstract A connection between the continuous translation equation and the Jordan non-measurable continuous functions is given.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"18 1","pages":"117 - 120"},"PeriodicalIF":0.9,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78954914","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 : 2017-12-01DOI: 10.1515/aupcsm-2017-0008
Edward Tutaj
Abstract We define and study some simple structures which we call likens and which are conceptually near to both sets of natural numbers, i.e. ℕ with addition and ℕ* = ℕ {0} with multiplication. It appears that there are many different likens, which makes it possible to look on usual natural numbers from a more general point of view. In particular, we show that ℕ and ℕ* are related to some functionals on the space of likens. A similar idea is known for a long time as the Beurling generalized numbers. Our approach may be considered as a little more natural and more general, since it admits the finitely generated likens.
摘要我们定义并研究了一些简单的结构，它们在概念上近似于两组自然数，即具有加法的n和具有乘法的n * = n {0}。似乎有许多不同的类比，这使得从更一般的角度来看待通常的自然数成为可能。特别地，我们证明了在比较项空间上的一些泛函与n和n *有关。一个类似的思想在很长一段时间内被称为伯灵广义数。我们的方法可以被认为是更自然和更普遍的，因为它允许有限生成的比较。
{"title":"Likeℕ’s – a point of view on natural numbers","authors":"Edward Tutaj","doi":"10.1515/aupcsm-2017-0008","DOIUrl":"https://doi.org/10.1515/aupcsm-2017-0008","url":null,"abstract":"Abstract We define and study some simple structures which we call likens and which are conceptually near to both sets of natural numbers, i.e. ℕ with addition and ℕ* = ℕ {0} with multiplication. It appears that there are many different likens, which makes it possible to look on usual natural numbers from a more general point of view. In particular, we show that ℕ and ℕ* are related to some functionals on the space of likens. A similar idea is known for a long time as the Beurling generalized numbers. Our approach may be considered as a little more natural and more general, since it admits the finitely generated likens.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"115 1","pages":"115 - 95"},"PeriodicalIF":0.9,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74899160","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 : 2017-11-28DOI: 10.1515/aupcsm-2017-0006
R. Kulkarni
Abstract In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.
{"title":"Intersect a quartic to extract its roots","authors":"R. Kulkarni","doi":"10.1515/aupcsm-2017-0006","DOIUrl":"https://doi.org/10.1515/aupcsm-2017-0006","url":null,"abstract":"Abstract In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"10 1","pages":"73 - 76"},"PeriodicalIF":0.9,"publicationDate":"2017-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75586412","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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