Georgian Mathematical Journal最新文献

{"title":"On corrected Simpson-type inequalities via local fractional integrals","authors":"Abdelghani Lakhdari, Badreddine Meftah, Wedad Saleh","doi":"10.1515/gmj-2024-2030","DOIUrl":"https://doi.org/10.1515/gmj-2024-2030","url":null,"abstract":"The paper discusses corrected Simpson-type inequalities on fractal sets. Based on an introduced identity, we establish some error bounds for the considered formula using the generalized <jats:italic>s</jats:italic>-convexity and <jats:italic>s</jats:italic>-concavity of the local fractional derivative. Finally, we present some graphical representations justifying the established theoretical framework as well as some applications.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Action of higher derivations on semiprime rings","authors":"Shakir Ali, Vaishali Varshney","doi":"10.1515/gmj-2024-2026","DOIUrl":"https://doi.org/10.1515/gmj-2024-2026","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0341.png\"/> <jats:tex-math>{m,n}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the fixed positive integers and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0224.png\"/> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a ring. In 1978, Herstein proved that a 2-torsion free prime ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0224.png\"/> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is commutative if there is a nonzero derivation <jats:italic>d</jats:italic> of <jats:italic>R</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ϱ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ξ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">]</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0157.png\"/> <jats:tex-math>{[d(varrho),d(xi)]=0}</jats:tex-math> </jats:alternatives> </jats:inline-formula> for all <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>ϱ</m:mi> <m:mo>,</m:mo> <m:mi>ξ</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>R</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0243.png\"/> <jats:tex-math>{varrho,xiin R}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In this article, we study the above mentioned classical result for higher derivations and describe the structure of semiprime rings by using the invariance property of prime ideals under higher derivations. Precisely, apart from proving some other important results, we prove the following. Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msub> <m:mi>d</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo stretchy=\"false\">)</m:mo","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations","authors":"Fethi Soltani, Meriem Nenni","doi":"10.1515/gmj-2024-2031","DOIUrl":"https://doi.org/10.1515/gmj-2024-2031","url":null,"abstract":"In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">ℬ</m:mi> <m:mi>α</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2031_eq_0181.png\"/> <jats:tex-math>{mathscr{B}_{alpha}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> in the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian equation and the time-dependent Dunkl–Schrödinger equation. The resolution of these types of problems is based on the techniques of the transmutation operators on the Dunkl-type Fock space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi mathvariant=\"script\">ℱ</m:mi> <m:mi>α</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msup> <m:mi>ℂ</m:mi> <m:mi>d</m:mi> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2031_eq_0190.png\"/> <jats:tex-math>{mathscr{F}_{alpha}(mathbb{C}^{d})}</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The influence of c-subnormality subgroups on the structure of finite groups","authors":"Dana Jaraden, Ali Ateiwi, Jehad Jaraden","doi":"10.1515/gmj-2024-2036","DOIUrl":"https://doi.org/10.1515/gmj-2024-2036","url":null,"abstract":"Let <jats:italic>H</jats:italic> be a subgroup of a group <jats:italic>G</jats:italic>. We say that <jats:italic>H</jats:italic> is <jats:italic>c</jats:italic>-subnormal in <jats:italic>G</jats:italic> if there exists a subnormal subgroup <jats:italic>T</jats:italic> of <jats:italic>G</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>⁢</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0064.png\"/> <jats:tex-math>{HT=G}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>∩</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>⩽</m:mo> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0065.png\"/> <jats:tex-math>{Hcap Tleqslant H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0073.png\"/> <jats:tex-math>{H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the maximal normal subgroup of <jats:italic>G</jats:italic> which is contained in <jats:italic>H</jats:italic>. In this paper, we investigate the structure of a finite group <jats:italic>G</jats:italic> under the assumption that all maximal subgroups are <jats:italic>c</jats:italic>-subnormal subgroups and present some new conditions for supersolvability.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Timelike zero mean curvature surfaces in ℝ1 4","authors":"Seher Kaya","doi":"10.1515/gmj-2024-2028","DOIUrl":"https://doi.org/10.1515/gmj-2024-2028","url":null,"abstract":"Abstract We are interested in the solution of the Björling problem for timelike surfaces in R 1 4 mathbb{R}_{1}^{4} . The main contribution of the paper is to present new and many examples of timelike zero mean curvature surfaces and give their explicit parametric equations. In particular cases, one observes that the parametric equations of these surfaces coincide with the timelike minimal surfaces in Lorentz–Minkowski 3-space.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141360706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized derivation on semiprime and prime Banach algebras","authors":"Emine Koç Sögütcü","doi":"10.1515/gmj-2024-2027","DOIUrl":"https://doi.org/10.1515/gmj-2024-2027","url":null,"abstract":"Abstract In this study, the commutativity conditions with generalized derivations, which have not been examined before, are discussed. Under these conditions, the subject of generalized derivations in (semi)prime Banach algebras is studied. New fundamental results will be provided for researchers in this field and generalize some of the results found in the literature.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141357019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix","authors":"S. Bouzidi, Ines Walha","doi":"10.1515/gmj-2024-2029","DOIUrl":"https://doi.org/10.1515/gmj-2024-2029","url":null,"abstract":"Abstract In this paper, we are interested to formulate new assumptions on the entries of an unbounded 3 × 3 3times 3 block operator matrix defined with a maximal domain on the product of Banach spaces guaranteeing its corresponding Frobenius–Schur formula. Our approach allows us to derive some original stability results intervening in the theory of perturbed lower semi-Fredholm operators involving the concept of a measure of non-strict cosingularity perturbation. A new technique is presented to investigate the Weidmann and defect essential spectra of the closure of such model of operator matrix via new criterion of perturbation.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141358483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions","authors":"R. Guefaifia, S. Boulaaras, Rashid Jan","doi":"10.1515/gmj-2024-2025","DOIUrl":"https://doi.org/10.1515/gmj-2024-2025","url":null,"abstract":"\u0000 In this work, we establish a theorem concerning the extension of positive weak solutions for a stationary fractional Laplacian problem featuring weight functions that change sign. Additionally, we introduce novel conditions to ensure the existence of a positive solution for the given problem. These conditions are derived utilizing the approach of sub-super solutions, thereby extending and complementing existing results in the literature.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140962280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain","authors":"Akanksha Kesarwani, Rasmita Kar","doi":"10.1515/gmj-2024-2022","DOIUrl":"https://doi.org/10.1515/gmj-2024-2022","url":null,"abstract":"\u0000 <jats:p>In this paper, we study the following elliptic problem involving the (<jats:inline-formula id=\"j_gmj-2024-2022_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mrow>\u0000 <m:mi>p</m:mi>\u0000 <m:mo>⁢</m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mi>y</m:mi>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 <m:mo>,</m:mo>\u0000 <m:mrow>\u0000 <m:mi>q</m:mi>\u0000 <m:mo>⁢</m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mi>y</m:mi>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2022_eq_0339.png\"/>\u0000 <jats:tex-math>{p(y),q(y)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>)-Laplacian operator:</jats:p>\u0000 <jats:p>\u0000 <jats:disp-formula id=\"j_gmj-2024-2022_eq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mo>{</m:mo>\u0000 <m:mtable columnspacing=\"0pt\" displaystyle=\"true\" rowspacing=\"0pt\">\u0000 <m:mtr>\u0000 <m:mtd columnalign=\"right\">\u0000 <m:mrow>\u0000 <m:mrow>\u0000 <m:mrow>\u0000 <m:mo>-</m:mo>\u0000 <m:mrow>\u0000 <m:mi>div</m:mi>\u0000 <m:mo>⁡</m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mrow>\u0000 <m:mi>a</m:mi>\u0000 <m:mo>⁢</m:mo>\u0000 <m:mrow>\u0000 ","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140655328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function","authors":"Alexander Kharazishvili","doi":"10.1515/gmj-2024-2023","DOIUrl":"https://doi.org/10.1515/gmj-2024-2023","url":null,"abstract":"\u0000 It is shown that there exists a Mazurkiewicz subset of\u0000the Euclidean plane containing the graph of some Sierpiński–Zygmund function.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140659791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}