Arab Journal of Mathematical Sciences最新文献

{"title":"Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces","authors":"G. A. Okeke, Daniel Francis","doi":"10.1108/AJMS-10-2020-0098","DOIUrl":"https://doi.org/10.1108/AJMS-10-2020-0098","url":null,"abstract":"PurposeThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.Research limitations/implicationsThe results are theoretical and analytical.Practical implicationsThe results were applied to solving nonlinear integral equations.Social implicationsThe results has several social applications.Originality/valueThe results of this paper are new.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43799232","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}

{"title":"Multistep-type construction of fixed point for multivalued ρ-quasi-contractive-like maps in modular function spaces","authors":"H. Akewe, H. Olaoluwa","doi":"10.1108/AJMS-07-2020-0026","DOIUrl":"https://doi.org/10.1108/AJMS-07-2020-0026","url":null,"abstract":"PurposeIn this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that PρT, an associate multivalued map, is a ρ-contractive-like mapping.Design/methodology/approachThe concepts of relative ρ-stability and weak ρ-stability are introduced, and conditions in which these multistep iterations are relatively ρ-stable, weakly ρ-stable and ρ-stable are established for the newly introduced strong ρ-quasi-contractive-like class of maps.FindingsNoor type, Ishikawa type and Mann type iterative sequences are deduced as corollaries in this study.Originality/valueThe results obtained in this work are complementary to those proved in normed and metric spaces in the literature.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47398599","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}

{"title":"Generalized cyclic contractions and coincidence points involving a control function on partial metric spaces","authors":"S. K. Mohanta","doi":"10.1108/ajms-07-2020-0023","DOIUrl":"https://doi.org/10.1108/ajms-07-2020-0023","url":null,"abstract":"PurposeIn this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.Design/methodology/approachTheoretical method.FindingsWe establish some coincidence points and common fixed point results in partial metric spaces.Originality/valueResults of this study are new and interesting.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41806896","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}

{"title":"Further fresh and general traveling wave solutions to some fractional order nonlinear evolution equations in mathematical physics","authors":"T. Islam, Armina Akter","doi":"10.1108/ajms-09-2020-0078","DOIUrl":"https://doi.org/10.1108/ajms-09-2020-0078","url":null,"abstract":"PurposeFractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.Design/methodology/approachThe rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.FindingsAchieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.Originality/valueThe rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41404939","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}

{"title":"On classification of (n + 6)-dimensional nilpotent n-Lie algebras of class 2 with n ≥ 4","authors":"M. Jamshidi, F. Saeedi, H. Darabi","doi":"10.1108/AJMS-09-2020-0075","DOIUrl":"https://doi.org/10.1108/AJMS-09-2020-0075","url":null,"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose</jats:title><jats:p>The purpose of this paper is to determine the structure of nilpotent <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mrow><m:mo stretchy=\"true\">(</m:mo><m:mrow><m:mi>n</m:mi><m:mo>+</m:mo><m:mn>6</m:mn></m:mrow><m:mo stretchy=\"true\">)</m:mo></m:mrow></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-09-2020-0075005.tif\" /></jats:inline-formula>-dimensional <jats:italic>n</jats:italic>-Lie algebras of class 2 when <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mi>n</m:mi><m:mo>≥</m:mo><m:mn>4</m:mn></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-09-2020-0075006.tif\" /></jats:inline-formula>.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design/methodology/approach</jats:title><jats:p>By dividing a nilpotent <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mrow><m:mo stretchy=\"true\">(</m:mo><m:mrow><m:mi>n</m:mi><m:mo>+</m:mo><m:mn>6</m:mn></m:mrow><m:mo stretchy=\"true\">)</m:mo></m:mrow></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-09-2020-0075007.tif\" /></jats:inline-formula>-dimensional <jats:italic>n</jats:italic>-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mrow><m:mo stretchy=\"true\">(</m:mo><m:mrow><m:mi>n</m:mi><m:mo>+</m:mo><m:mn>5</m:mn></m:mrow><m:mo stretchy=\"true\">)</m:mo></m:mrow></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-09-2020-0075008.tif\" /></jats:inline-formula> dimensional <jats:italic>n</jats:italic>-Lie algebra of class 2. Given that the authors have the structure of nilpotent <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mrow><m:mo stretchy=\"true\">(</m:mo><m:mrow><m:mi>n</m:mi><m:mo>+</m:mo><m:mn>5</m:mn></m:mrow><m:mo stretchy=\"true\">)</m:mo></m:mrow></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-09-2020-0075009.tif\" /></jats:inline-formula>-dimensional <jats:italic>n</jats:italic>-Lie algebras of class 2, the authors have access to the structure of the desired algebras.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings</jats:title><jats:p>In this paper, for each <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mi>n</m:mi><m:mo>≥</m:mo><m:mn>4</m:mn></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-09-2020-0075010.tif\" /></jats:inline-formula>, the authors have found 24 nilpotent <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mrow><m:mo str","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42844540","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}

{"title":"A direct computation of a certain family of integrals","authors":"L. Fornari, E. Laeng, V. Pata","doi":"10.1108/AJMS-01-2021-0019","DOIUrl":"https://doi.org/10.1108/AJMS-01-2021-0019","url":null,"abstract":"PurposeThe authors propose a rather elementary method to compute a family of integrals on the half line, involving positive powers of sin x and negative powers of x, depending on the integer parameters n≥q≥1.Design/methodology/approachCombinatorics, sine and cosine integral functions.FindingsThe authors prove an explicit formula to evaluate sinc-type integrals.Originality/valueThe proof is not present in the current literature, and it could be of interest for a large audience.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47523240","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}

{"title":"Further study on the Brück conjecture and some non-linear complex differential equations","authors":"D. C. Pramanik, Kapil Roy","doi":"10.1108/AJMS-08-2020-0047","DOIUrl":"https://doi.org/10.1108/AJMS-08-2020-0047","url":null,"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose</jats:title><jats:p>The purpose of this current paper is to deal with the study of non-constant entire solutions of some non-linear complex differential equations in connection to Brück conjecture, by using the theory of complex differential equation. The results generalize the results due to Pramanik <jats:italic>et al.</jats:italic></jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design/methodology/approach</jats:title><jats:p>39B32, 30D35.</jats:p></jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings</jats:title><jats:p>In the current paper, we mainly study the Brück conjecture and the various works that confirm this conjecture. In our study we find that the conjecture can be generalized for differential monomials under some additional conditions and it generalizes some works related to the conjecture. Also we can take the complex number <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mi>a</m:mi></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-08-2020-0047901.tif\" /></jats:inline-formula> in the conjecture to be a small function. More precisely, we obtain a result which can be restate in the following way: Let <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mi>f</m:mi></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-08-2020-0047902.tif\" /></jats:inline-formula> be a non-constant entire function such that <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:msub><m:mi>σ</m:mi><m:mn>2</m:mn></m:msub><m:mrow><m:mo stretchy=\"false\">(</m:mo><m:mi>f</m:mi><m:mo stretchy=\"false\">)</m:mo></m:mrow><m:mo><</m:mo><m:mi>∞</m:mi></m:mrow></m:math><jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"AJMS-08-2020-0047903.tif\" /></jats:inline-formula>, <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:msub><m:mi>σ</m:mi><m:mn>2</m:mn></m:msub><m:mrow><m:mo stretchy=\"false\">(</m:mo><m:mi>f</m:mi><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=\"AJMS-08-2020-0047904.tif\" /></jats:inline-formula> is not a positive integer and <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mi>δ</m:mi><m:mrow><m:mo stretchy=\"true\">(</m:mo><m:mrow><m:mn>0</m:mn><m:mo>,</m:mo><m:mtext> </m:mtext><m:mi>f</m:mi></m:mrow><m:mo stretchy=\"true\">)</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=\"AJMS-08-2020-0047905.tif\" /></jats:inline-formula>. Let <jats:inline-formula><m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"><m:mrow><m:mi>M</m:mi><m:mrow><m:mo stretchy=\"false\">[</m:mo><m:mi>f</m:mi><m:mo stretchy=\"false\">]</m:mo></m:mrow></m:mro","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46288666","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}

{"title":"On a class of non-local discrete boundary value problem","authors":"A. Ourraoui, A. Ayoujil","doi":"10.1108/ajms-06-2020-0003","DOIUrl":"https://doi.org/10.1108/ajms-06-2020-0003","url":null,"abstract":"PurposeIn this article, the authors discuss the existence and multiplicity of solutions for an anisotropic discrete boundary value problem in T-dimensional Hilbert space. The approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.Design/methodology/approachThe approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.FindingsThe authors study the existence of results for a discrete problem, with two boundary conditions type. Accurately, the authors have proved the existence of at least three solutions.Originality/valueAn other feature is that problem is with non-local term, which makes some difficulties in the proof of our results.","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1108/ajms-06-2020-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47873234","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}

{"title":"On warped product bi-slant submanifolds of Kenmotsu manifolds","authors":"S. Uddin, I. Mihai, A. Mihai","doi":"10.1016/J.AJMSC.2019.06.001","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.06.001","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.06.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45561843","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}

{"title":"Toeplitz and slant Toeplitz operators on the polydisk","authors":"M. Hazarika, Sougata Marik","doi":"10.1016/J.AJMSC.2019.02.003","DOIUrl":"https://doi.org/10.1016/J.AJMSC.2019.02.003","url":null,"abstract":"","PeriodicalId":36840,"journal":{"name":"Arab Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/J.AJMSC.2019.02.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43626559","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}