Pub Date : 2022-04-15DOI: 10.24193/mathcluj.2022.1.11
Sundas Khan, H. Budak
We establish some Hermite-Hadamard type inequalities for multiplicative convex functions. First, we obtain two equality for $^{ast }$ differentiable functions. Then using these inequalities and multiplicative convex functions, we establish some inequalities related to the right and left hand side of Hermite-Hadamard inequality for multiplicative integrals.
{"title":"On midpoint and trapezoid type inequalities for multiplicative integrals","authors":"Sundas Khan, H. Budak","doi":"10.24193/mathcluj.2022.1.11","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.1.11","url":null,"abstract":"We establish some Hermite-Hadamard type inequalities for multiplicative convex functions. First, we obtain two equality for $^{ast }$ differentiable functions. Then using these inequalities and multiplicative convex functions, we establish some inequalities related to the right and left hand side of Hermite-Hadamard inequality for multiplicative integrals.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46305197","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 : 2022-04-15DOI: 10.24193/mathcluj.2022.1.04
Marziyeh Atashkar, Y. Talebi
We introduce the notion of FI-retractable modules which is a generalization of retractable modules. A module is called FI-retractable if for every nonzero fully invariant submodule N of M, Hom(M,N) is not 0. Wee continue the study of FI-retractable modules. Amongst other structural properties, we also deal direct sums and direct summands of FI-retractable modules. The last section of the paper is devoted to study of End(M), such that M is FI-retractable.
{"title":"On FI-retractable modules","authors":"Marziyeh Atashkar, Y. Talebi","doi":"10.24193/mathcluj.2022.1.04","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.1.04","url":null,"abstract":"We introduce the notion of FI-retractable modules which is a generalization of retractable modules. A module is called FI-retractable if for every nonzero fully invariant submodule N of M, Hom(M,N) is not 0. Wee continue the study of FI-retractable modules. Amongst other structural properties, we also deal direct sums and direct summands of FI-retractable modules. The last section of the paper is devoted to study of End(M), such that M is FI-retractable.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46659212","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 : 2022-04-15DOI: 10.24193/mathcluj.2022.1.01
T. Al-Hawary
We explore the operations of deletion, contraction, direct sum and ordered sum of greedoids. Moreover, we introduce the notion of balanced greedoid and give a necessary and sufficient condition for the direct sum and ordered sum of balanced greedoids to be balanced.
{"title":"Operations on greedoids","authors":"T. Al-Hawary","doi":"10.24193/mathcluj.2022.1.01","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.1.01","url":null,"abstract":"We explore the operations of deletion, contraction, direct sum and ordered sum of greedoids. Moreover, we introduce the notion of balanced greedoid and give a necessary and sufficient condition for the direct sum and ordered sum of balanced greedoids to be balanced.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43167440","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 : 2022-04-15DOI: 10.24193/mathcluj.2022.1.07
Abdelatif Boutiara, Maamar Benbachir, K. Guerbati
We give some existence and regularity results for a system of a new class of hybrid Caputo-Hadamard fractional differential equations under hybrid boundary conditions. The technique of investigation is essentially based on the use of a well known hybrid fixed point theorem.
{"title":"On the solvability of a system of Caputo-Hadamard fractional hybrid differential equations subject to some hybrid boundary conditions","authors":"Abdelatif Boutiara, Maamar Benbachir, K. Guerbati","doi":"10.24193/mathcluj.2022.1.07","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.1.07","url":null,"abstract":"We give some existence and regularity results for a system of a new class of hybrid Caputo-Hadamard fractional differential equations under hybrid boundary conditions. The technique of investigation is essentially based on the use of a well known hybrid fixed point theorem.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46080649","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 : 2022-04-15DOI: 10.24193/mathcluj.2022.1.08
Hocine Gabsi, A. Ardjouni, A. Djoudi
We offer existence criteria and sufficient conditions, so that the trivial solution of the differential system with several delays of feedback control is asymptotically stable. Here the fixed point technique is a practical method for this purpose. When these results are applied to some special delay mathematics models, some new results are obtained, and many known results are improved. Lastly, we provide an example that illustrates our results.
{"title":"Fixed points and stability of a class of nonlinear differential systems with several delays of feedback control","authors":"Hocine Gabsi, A. Ardjouni, A. Djoudi","doi":"10.24193/mathcluj.2022.1.08","DOIUrl":"https://doi.org/10.24193/mathcluj.2022.1.08","url":null,"abstract":"We offer existence criteria and sufficient conditions, so that the trivial solution of the differential system with several delays of feedback control is asymptotically stable. Here the fixed point technique is a practical method for this purpose. When these results are applied to some special delay mathematics models, some new results are obtained, and many known results are improved. Lastly, we provide an example that illustrates our results.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42772283","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.13
Tayeb Lakroumbe, M. Abdelli, Naima Louhibi, Mounir Bahlil
We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.
{"title":"Well-posedness and general energy decay of solutions for a Petrovsky equation with a nonlinear strong dissipation","authors":"Tayeb Lakroumbe, M. Abdelli, Naima Louhibi, Mounir Bahlil","doi":"10.24193/mathcluj.2021.2.13","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.13","url":null,"abstract":"We consider a nonlinear Petrovsky equation in a bounded domain with a strong dissipation, and prove the existence and the uniqueness of the solution using the energy method combined with the Faedo-Galerkin procedure under certain assumptions. Furthermore, we study the asymptotic behaviour of the solutions using a perturbed energy method.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48553403","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.14
G. Olteanu
For a group G, a G-graded ring R and a finite left G-set A, we study the strong regularity of the smash product of R and A.
对于一个群G，一个G-分次环R和一个有限左G-集a，我们研究了R和a的砸积的强正则性。
{"title":"Strong regularity of smash products associated with G-set gradings","authors":"G. Olteanu","doi":"10.24193/mathcluj.2021.2.14","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.14","url":null,"abstract":"For a group G, a G-graded ring R and a finite left G-set A, we study the strong regularity of the smash product of R and A.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45713343","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.07
Abdelatif Boutiara, Maamar Benbachir, K. Guerbati
The purpose of this paper is to investigate the existence and uniqueness of solutions for a new class of nonlinear fractional differential equations involving Hilfer fractional operator with fractional integral boundary conditions. Our analysis relies on classical fixed point theorems and the Boyd-Wong nonlinear contraction. At the end, an illustrative example is presented. The boundary conditions introduced in this work are of quite general nature and can be reduce to many special cases by fixing the parameters involved in the conditions.
{"title":"Boundary value problems for Hilfer fractional differential equations with Katugampola fractional integral and anti-periodic conditions","authors":"Abdelatif Boutiara, Maamar Benbachir, K. Guerbati","doi":"10.24193/mathcluj.2021.2.07","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.07","url":null,"abstract":"The purpose of this paper is to investigate the existence and uniqueness of solutions for a new class of nonlinear fractional differential equations involving Hilfer fractional operator with fractional integral boundary conditions. Our analysis relies on classical fixed point theorems and the Boyd-Wong nonlinear contraction. At the end, an illustrative example is presented. The boundary conditions introduced in this work are of quite general nature and can be reduce to many special cases by fixing the parameters involved in the conditions.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47275970","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.01
Sakha A. Alkabouss, Boualem Benseba, Nacira Berbara, S. Earp-Lynch, F. Luca
We investigate the Diophantine equation x^2 −kxy + ky^2 + ly = 0 for integers k and l with k even. We give a characterization of the positive solutions of this equation in terms of k and l. We also consider the same equation for other values of k and l.
{"title":"A note on the Diophantine Equation x^2-kxy+ky^2+ly=0","authors":"Sakha A. Alkabouss, Boualem Benseba, Nacira Berbara, S. Earp-Lynch, F. Luca","doi":"10.24193/mathcluj.2021.2.01","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.01","url":null,"abstract":"We investigate the Diophantine equation x^2 −kxy + ky^2 + ly = 0 for integers k and l with k even. We give a characterization of the positive solutions of this equation in terms of k and l. We also consider the same equation for other values of k and l.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44127324","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 : 2021-11-25DOI: 10.24193/mathcluj.2021.2.03
Benaissa Bouharket, M. Sarıkaya
In this paper, we give some new generalizations of the weighted bilinear Hardy inequality by using certain weighted mean operators.
本文利用某些加权均值算子，给出了加权双线性Hardy不等式的一些新的推广。
{"title":"A generalization of weighted bilinear Hardy inequality","authors":"Benaissa Bouharket, M. Sarıkaya","doi":"10.24193/mathcluj.2021.2.03","DOIUrl":"https://doi.org/10.24193/mathcluj.2021.2.03","url":null,"abstract":"In this paper, we give some new generalizations of the weighted bilinear Hardy inequality by using certain weighted mean operators.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43000634","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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