Pub Date : 2023-01-01DOI: 10.2478/aupcsm-2023-0004
Bharat Bhushan, G. Sandhu, D. Kumar
Abstract In this article, we introduce the notion of centrally-extended generalized Jordan derivations and characterize the structure of a prime ring (resp. *-prime ring) R that admits a centrally-extended generalized Jordan derivation F satisfying [F(x), x] ∈ Z(R) (resp. [F(x), x*] ∈ Z(R)) for all x ∈ R.
{"title":"Centrally-extended generalized Jordan derivations in rings","authors":"Bharat Bhushan, G. Sandhu, D. Kumar","doi":"10.2478/aupcsm-2023-0004","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0004","url":null,"abstract":"Abstract In this article, we introduce the notion of centrally-extended generalized Jordan derivations and characterize the structure of a prime ring (resp. *-prime ring) R that admits a centrally-extended generalized Jordan derivation F satisfying [F(x), x] ∈ Z(R) (resp. [F(x), x*] ∈ Z(R)) for all x ∈ R.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"2013 1","pages":"33 - 47"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73868958","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0002
L. Rakhimi, Abdelmajid Khadari, R. Daher
Abstract The main result of the paper is the proof of the equivalence theorem for a K-functional and a modulus of smoothness for the Deformed Hankel Transform. Before that, we introduce the K-functional associated to the Deformed Hankel Transform.
{"title":"K-functional related to the Deformed Hankel Transform","authors":"L. Rakhimi, Abdelmajid Khadari, R. Daher","doi":"10.2478/aupcsm-2023-0002","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0002","url":null,"abstract":"Abstract The main result of the paper is the proof of the equivalence theorem for a K-functional and a modulus of smoothness for the Deformed Hankel Transform. Before that, we introduce the K-functional associated to the Deformed Hankel Transform.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"12 2 1","pages":"13 - 20"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83485441","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0001
B. Kartal
Abstract In this paper, a general theorem gives necessary and sufficient conditions for the inclusion relation between φ – |A, β ; δ|k and φ – |B, β ; δ|k methods is proved.
摘要本文给出了φ - | a， β;δ|k和φ - |B， β;证明了δ|k方法。
{"title":"Necessary and sufficient conditions for the inclusion relation between two summability methods","authors":"B. Kartal","doi":"10.2478/aupcsm-2023-0001","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0001","url":null,"abstract":"Abstract In this paper, a general theorem gives necessary and sufficient conditions for the inclusion relation between φ – |A, β ; δ|k and φ – |B, β ; δ|k methods is proved.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"12 1","pages":"5 - 11"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82242376","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}
Abstract In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity variable η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).
{"title":"Existence results of self-similar solutions of the space-fractional diffusion equation involving the generalized Riesz-Caputo fractional derivative","authors":"Nora Ouagueni, Yacine Arioua, Noureddine Benhamidouche","doi":"10.2478/aupcsm-2023-0005","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0005","url":null,"abstract":"Abstract In this paper, we have discussed the problem of existence and uniqueness of solutions under the self-similar form to the space-fractional diffusion equation. The space-fractional derivative which will be used is the generalized Riesz-Caputo fractional derivative. Based on the similarity variable η, we have introduced the equation satisfied by the self-similar solutions for the aforementioned problem. To study the existence and uniqueness of self-similar solutions for this problem, we have applied some known fixed point theorems (i.e. Banach’s contraction principle, Schauder’s fixed point theorem and the nonlinear alternative of Leray-Schauder type).","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"1 1","pages":"49 - 74"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80917549","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0003
Moustapha Camara, Moussa Fall, Oumar Sall
Abstract We give an algebraic description of the set of algebraic points of degree at most d over ℚ on hyperelliptic curves y2 = x5 + n2.
摘要给出了超椭圆曲线y2 = x5 + n2上最多为d / π次的代数点集的代数描述。
{"title":"Algebraic points on the hyperelliptic curves y2 = x5 + n2","authors":"Moustapha Camara, Moussa Fall, Oumar Sall","doi":"10.2478/aupcsm-2023-0003","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0003","url":null,"abstract":"Abstract We give an algebraic description of the set of algebraic points of degree at most d over ℚ on hyperelliptic curves y2 = x5 + n2.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"5 1","pages":"21 - 31"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73396357","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0010
Hikmet Seyhan Özarslan
Abstract In the present paper, a theorem on θ −| T; δ | k summability method of an infinite series is proved, and also by using this method, a result on summability of a trigonometric Fourier series is obtained.
{"title":"On absolute summability of infinite series and Fourier series","authors":"Hikmet Seyhan Özarslan","doi":"10.2478/aupcsm-2023-0010","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0010","url":null,"abstract":"Abstract In the present paper, a theorem on θ −| T; δ | k summability method of an infinite series is proved, and also by using this method, a result on summability of a trigonometric Fourier series is obtained.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"161 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135497660","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0007
A. Rezaei, H. Kim, A. Saeid
Abstract In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.
{"title":"Independence concepts for groupoids","authors":"A. Rezaei, H. Kim, A. Saeid","doi":"10.2478/aupcsm-2023-0007","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0007","url":null,"abstract":"Abstract In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"46 1","pages":"87 - 98"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87561934","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0006
P. Pasteczka
Abstract Based on the notion of thin sets introduced recently by T. Banakh, Sz. Głąb, E. Jabłońska and J. Swaczyna we deliver a study of the infinite single-message transmission protocols. Such protocols are associated with a set of admissible messages (i.e. subsets of the Cantor cube ℤ2ω). Using Banach-Mazur games we prove that all protocols detecting errors are Baire spaces and generic (in particular maximal) ones are not neither Borel nor meager. We also show that the Cantor cube can be decomposed to two thin sets which can be considered as the infinite counterpart of the parity bit. This result is related to so-called xor-sets defined by D. Niwiński and E. Kopczyński in 2014.
基于T. Banakh, Sz。Głąb, E. Jabłońska和J. Swaczyna我们提供了无限单消息传输协议的研究。这样的协议与一组可接受的消息(即康托立方的子集)相关联。利用Banach-Mazur博弈，我们证明了所有检测错误的协议都是Baire空间，而一般的(特别是极大的)协议既不是Borel也不是微薄的。我们还证明了康托立方体可以分解为两个薄集，这两个薄集可以被认为是奇偶位的无限对偶。这一结果与D. Niwiński和E. Kopczyński在2014年定义的所谓xor集有关。
{"title":"Error recognition in the Cantor cube","authors":"P. Pasteczka","doi":"10.2478/aupcsm-2023-0006","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0006","url":null,"abstract":"Abstract Based on the notion of thin sets introduced recently by T. Banakh, Sz. Głąb, E. Jabłońska and J. Swaczyna we deliver a study of the infinite single-message transmission protocols. Such protocols are associated with a set of admissible messages (i.e. subsets of the Cantor cube ℤ2ω). Using Banach-Mazur games we prove that all protocols detecting errors are Baire spaces and generic (in particular maximal) ones are not neither Borel nor meager. We also show that the Cantor cube can be decomposed to two thin sets which can be considered as the infinite counterpart of the parity bit. This result is related to so-called xor-sets defined by D. Niwiński and E. Kopczyński in 2014.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"28 3 1","pages":"75 - 86"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79817134","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0008
Noureddine Azzouz, B. Benaissa, A. Senouci
Abstract In the present work, some Hardy-type integral inequalities were proved for two parameters of summation q ≤ p < 0 and p < 0, q > 0. In addition, some two-sided estimates are obtained.
{"title":"Some Hardy type integral inequalities with two parameters of summation","authors":"Noureddine Azzouz, B. Benaissa, A. Senouci","doi":"10.2478/aupcsm-2023-0008","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0008","url":null,"abstract":"Abstract In the present work, some Hardy-type integral inequalities were proved for two parameters of summation q ≤ p < 0 and p < 0, q > 0. In addition, some two-sided estimates are obtained.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"84 1","pages":"99 - 109"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83852364","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 : 2023-01-01DOI: 10.2478/aupcsm-2023-0009
Sezer Erdem, Serkan Demiriz
Abstract This study includes the new Banach space ℒ˜sq$$tilde {cal L}_s^q$$ designed as the domain in 𝓛s space of the 4d (4-dimensional) q-Cesàro matrix obtained as the q-analog of the well-known 4d Cesàro matrix. After showing the completeness of the aforementioned space, giving some inclusion relations, determining the fundamental set of this space and calculating the duals, finally, some matrix transformations related to the new space were characterized.
{"title":"q-Cesàro double sequence space ℒ˜sq$$tilde {cal L}_s^q$$ derived by q-analog","authors":"Sezer Erdem, Serkan Demiriz","doi":"10.2478/aupcsm-2023-0009","DOIUrl":"https://doi.org/10.2478/aupcsm-2023-0009","url":null,"abstract":"Abstract This study includes the new Banach space ℒ˜sq$$tilde {cal L}_s^q$$ designed as the domain in 𝓛s space of the 4d (4-dimensional) q-Cesàro matrix obtained as the q-analog of the well-known 4d Cesàro matrix. After showing the completeness of the aforementioned space, giving some inclusion relations, determining the fundamental set of this space and calculating the duals, finally, some matrix transformations related to the new space were characterized.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"3 1","pages":"111 - 126"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74445409","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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