In this paper, we introduce mixed R-monotone property of a mapping and utilize the same to investigate existence and uniqueness of coupled fixed points in a metric space endowed with a binary relation R. Moreover, we present some coupled fixed point results for mappings without mixed monotone property using relation-theoretic approach. Our results generalize some well-known coupled fixed points theorems. Further, we give some illustrative examples in support of our results.
{"title":"RELATION-THEORETIC COUPLED FIXED POINT THEOREMS","authors":"Faruk Sk, Faizan AHMAD KHAN, Qamrul HAQ KHAN","doi":"10.54379/jma-2022-3-4","DOIUrl":"https://doi.org/10.54379/jma-2022-3-4","url":null,"abstract":"In this paper, we introduce mixed R-monotone property of a mapping and utilize the same to investigate existence and uniqueness of coupled fixed points in a metric space endowed with a binary relation R. Moreover, we present some coupled fixed point results for mappings without mixed monotone property using relation-theoretic approach. Our results generalize some well-known coupled fixed points theorems. Further, we give some illustrative examples in support of our results.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47699808","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}
In this paper, we introduce a new form of discrete Hilbert inequality for three variables, also, we prove that the constant which appears on the right hand of inequality is the best constant. Also, the reverse form and equivalent forms are, obtained.
{"title":"NEW DISCRETE FORM OF HILBERT INEQUALITY FOR THREE VARIABLES","authors":"Nizar KH. AL-OUSHOUSH","doi":"10.54379/jma-2022-3-5","DOIUrl":"https://doi.org/10.54379/jma-2022-3-5","url":null,"abstract":"In this paper, we introduce a new form of discrete Hilbert inequality for three variables, also, we prove that the constant which appears on the right hand of inequality is the best constant. Also, the reverse form and equivalent forms are, obtained.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42824633","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}
In this article, we introduce the concept of tripled controlled V -metric spaces and study Kannan type contractions in this new structure. Also, we extend the concept of Kannan type contractions to KannanPresi´c type contractions. Our results modify some known ones in the literature. To support our main results, an example and an application in integral equations are presented.
{"title":"KANNAN AND KANNAN-PRESIC TYPE CONTRACTIONS IN TRIPLED ´ CONTROLLED V -METRIC SPACES","authors":"A. Karami, S. Sedghi, Vahid Parvaneh","doi":"10.54379/jma-2022-3-1","DOIUrl":"https://doi.org/10.54379/jma-2022-3-1","url":null,"abstract":"In this article, we introduce the concept of tripled controlled V -metric spaces and study Kannan type contractions in this new structure. Also, we extend the concept of Kannan type contractions to KannanPresi´c type contractions. Our results modify some known ones in the literature. To support our main results, an example and an application in integral equations are presented.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47115208","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}
Hamdan Al Sulaimani, K. Anaya, Cyril Dennis Enyi, Soh Edwin Mukiawa
In this paper, we establish an optimal and general decay result for the energy of a viscoelastic equation exhibiting a strong time-dependent delay. This is achieved by considering a minimal condition on the relaxation function g. The exponential and polynomial decay rates are obtained as special cases.The theoretical computations are supported with a numerical analysis of the problem under consideration. This work extends and generalizes some recent results in the literature.
{"title":"A GENERAL AND OPTIMAL DECAY RESULT FOR A VISCOELASTIC EQUATION WITH A STRONG TIME DEPENDENT DELAY","authors":"Hamdan Al Sulaimani, K. Anaya, Cyril Dennis Enyi, Soh Edwin Mukiawa","doi":"10.54379/jma-2022-3-3","DOIUrl":"https://doi.org/10.54379/jma-2022-3-3","url":null,"abstract":"In this paper, we establish an optimal and general decay result for the energy of a viscoelastic equation exhibiting a strong time-dependent delay. This is achieved by considering a minimal condition on the relaxation function g. The exponential and polynomial decay rates are obtained as special cases.The theoretical computations are supported with a numerical analysis of the problem under consideration. This work extends and generalizes some recent results in the literature.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47056132","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}
The theory of dynamical systems is one of the most important theorems of scientific research because it relies heavily on most of the major fields of applied mathematics to give a sufficiently broad view of reality, but it still poses some problems, especially with regard to the modeling of certain physical phenomena. Since most of these systems are designed as continuous or discrete dynamic systems with large dimensions and multiple bifurcation parameters, researchers face major problems in qualitative study. In this paper, we propose a method to study bifurcations of continuous three-dimensional dynamic systems in general and chaotic systems in particular, which contains many bifurcation parameters. This method is mainly based on the projection on the plane and on the appropriate bifurcation parameter.
{"title":"DYNAMIC ANALYSIS OF A CHAOTIC 3D QUADRATIC SYSTEM USING PLANAR PROJECTION.","authors":"Abdellah Menasri","doi":"10.54379/jma-2022-3-2","DOIUrl":"https://doi.org/10.54379/jma-2022-3-2","url":null,"abstract":"The theory of dynamical systems is one of the most important theorems of scientific research because it relies heavily on most of the major fields of applied mathematics to give a sufficiently broad view of reality, but it still poses some problems, especially with regard to the modeling of certain physical phenomena. Since most of these systems are designed as continuous or discrete dynamic systems with large dimensions and multiple bifurcation parameters, researchers face major problems in qualitative study. In this paper, we propose a method to study bifurcations of continuous three-dimensional dynamic systems in general and chaotic systems in particular, which contains many bifurcation parameters. This method is mainly based on the projection on the plane and on the appropriate bifurcation parameter.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43188091","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}
In this paper we study the boundedness of weighted Hardy operators Hα u and Hα u in local ”complementary” generalized variable exponent weighted Morrey spaces {M p(·),ω,ϕ {0} , characterized by variable exponent p(x), a general function ω(r) and a weight ϕ. We also study the boundedness of the commutators of Hα u and Hα u in the spaces {M p(·),ω,ϕ {0} .
{"title":"GENERALIZED WEIGHTED HARDY OPERATORS AND THEIR COMMUTATORS IN THE LOCAL ”COMPLEMENTARY” GENERALIZED VARIABLE EXPONENT WEIGHTED MORREY SPACES","authors":"C. Aykol, Zuleyxa O. AZIZOVA, ,. Hasanov","doi":"10.54379/jma-2022-1-2","DOIUrl":"https://doi.org/10.54379/jma-2022-1-2","url":null,"abstract":"In this paper we study the boundedness of weighted Hardy operators Hα u and Hα u in local ”complementary” generalized variable exponent weighted Morrey spaces {M p(·),ω,ϕ {0} , characterized by variable exponent p(x), a general function ω(r) and a weight ϕ. We also study the boundedness of the commutators of Hα u and Hα u in the spaces {M p(·),ω,ϕ {0} .","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49285011","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}
In this paper, we discuss the isometries of composition operators on the holomorphic general family function spaces F(p, q, s). First, we classify the isometric composition operators acting on a general Banach spaces. For 1 < p < 2, we display that an isometry of Cφ is caused only by a rotation of the disk. We scrutinize the previous work on the case for p ≥ 2. Also, we characterize many of the foregoing results about all α-Besov-type spaces F(p, αp − 2, s), α > 0. We exhibit that in every classes F(p, αp − 2, s) except for the Dirichlet space D = F(2, 0, 0), rotations are the only that produce isometries.
本文讨论了全纯一般族函数空间F(p, q, s)上复合算子的等距性。首先，对作用于一般Banach空间上的等距复合算子进行了分类。对于1 < p < 2，我们证明了Cφ的等距只由圆盘的旋转引起。对于p≥2的情况，我们仔细检查先前的工作。此外，我们还刻画了关于所有α- besov型空间F(p， αp−2,s)， α > 0的许多上述结果。我们证明了在所有类F(p， αp−2,s)中，除了Dirichlet空间D = F(2,0,0)，旋转是唯一产生等距的。
{"title":"ISOMETRIES ON SOME GENERAL FAMILY FUNCTION SPACES AMONG COMPOSITION OPERATORS","authors":"M. A. Bakhit","doi":"10.54379/jma-2022-1-1","DOIUrl":"https://doi.org/10.54379/jma-2022-1-1","url":null,"abstract":"In this paper, we discuss the isometries of composition operators on the holomorphic general family function spaces F(p, q, s). First, we classify the isometric composition operators acting on a general Banach spaces. For 1 < p < 2, we display that an isometry of Cφ is caused only by a rotation of the disk. We scrutinize the previous work on the case for p ≥ 2. Also, we characterize many of the foregoing results about all α-Besov-type spaces F(p, αp − 2, s), α > 0. We exhibit that in every classes F(p, αp − 2, s) except for the Dirichlet space D = F(2, 0, 0), rotations are the only that produce isometries.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41848070","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}
In this paper, we establish some regularity properties of the HardyLittlewood maximal operator including its boundedness on some subspaces of a Morrey-Sobolev space and a pointwise inequality involving the weak derivative of the maximal function.
{"title":"ON SOME REGULARITY PROPERTIES OF THE HARDY-LITTLEWOOD MAXIMAL OPERATOR","authors":"Berenger AKON KPATA","doi":"10.54379/jma-2022-1-3","DOIUrl":"https://doi.org/10.54379/jma-2022-1-3","url":null,"abstract":"In this paper, we establish some regularity properties of the HardyLittlewood maximal operator including its boundedness on some subspaces of a Morrey-Sobolev space and a pointwise inequality involving the weak derivative of the maximal function.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43534606","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}
In this article, we introduce generalized q−Sz´asz-Mirakjan operators and study their approximation properties. Based on the Voronovskaja’s theorem, we obtain quantitative estimates for these operators.
{"title":"APPROXIMATION BY GENERALIZED q-SZASZ-MIRAKJAN ´ OPERATORS","authors":"T. Khan, M. Saif, Shuzaat ALI KHAN","doi":"10.54379/jma-2021-6-2","DOIUrl":"https://doi.org/10.54379/jma-2021-6-2","url":null,"abstract":"In this article, we introduce generalized q−Sz´asz-Mirakjan operators and study their approximation properties. Based on the Voronovskaja’s theorem, we obtain quantitative estimates for these operators.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43519349","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}
A topological space X is called P-normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A : A −→ f(A) is a homeomorphism for each paracompact subspace A ⊆ X. We will investigate this property and produce some examples to illustrate the relation between P-normality and other weaker kinds of normality.
{"title":"P-Normality","authors":"Lutfi Kalantan, M. Mansouri","doi":"10.54379/jma-2021-6-1","DOIUrl":"https://doi.org/10.54379/jma-2021-6-1","url":null,"abstract":"A topological space X is called P-normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A : A −→ f(A) is a homeomorphism for each paracompact subspace A ⊆ X. We will investigate this property and produce some examples to illustrate the relation between P-normality and other weaker kinds of normality.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46627151","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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