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Dynamical behavior of one rational fifth-order difference equation 一类有理五阶差分方程的动力学行为
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-04-21 DOI: 10.15330/cmp.15.1.43-51
B. Oğul, D. Şi̇mşek
{"title":"Dynamical behavior of one rational fifth-order difference equation","authors":"B. Oğul, D. Şi̇mşek","doi":"10.15330/cmp.15.1.43-51","DOIUrl":"https://doi.org/10.15330/cmp.15.1.43-51","url":null,"abstract":"In this paper, we study the qualitative behavior of the rational recursive equation begin{equation*} x_{n+1}=frac{x_{n-4}}{pm1pm x_{n}x_{n-1}x_{n-2}x_{n-3}x_{n-4}}, quad n in mathbb{N}_{0}:={0}cupmathbb N, end{equation*} where the initial conditions are arbitrary nonzero real numbers. The main goal of this paper, is to obtain the forms of the solutions of the nonlinear fifth-order difference equations, where the initial conditions are arbitrary positive real numbers. Moreover, we investigate stability, boundedness, oscillation and the periodic character of these solutions. The results presented in this paper improve and extend some corresponding results in the literature.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72631811","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}
引用次数: 0
A study on conformal Ricci solitons and conformal Ricci almost solitons within the framework of almost contact geometry 几乎接触几何框架下共形Ricci孤子和共形Ricci几乎孤子的研究
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-04-12 DOI: 10.15330/cmp.15.1.31-42
S. Dey
{"title":"A study on conformal Ricci solitons and conformal Ricci almost solitons within the framework of almost contact geometry","authors":"S. Dey","doi":"10.15330/cmp.15.1.31-42","DOIUrl":"https://doi.org/10.15330/cmp.15.1.31-42","url":null,"abstract":"The goal of this paper is to find some important Einstein manifolds using conformal Ricci solitons and conformal Ricci almost solitons. We prove that a Kenmotsu metric as a conformal Ricci soliton is Einstein if it is an $eta$-Einstein or the potential vector field $V$ is infinitesimal contact transformation or collinear with the Reeb vector field $xi$. Next, we prove that a Kenmotsu metric as gradient conformal Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariant. Finally, we have embellished an example to illustrate the existence of conformal Ricci soliton and gradient almost conformal Ricci soliton on Kenmotsu manifold.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89674471","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}
引用次数: 0
Asymptotic estimates for the widths of classes of functions of high smothness 高平滑函数类宽度的渐近估计
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-04-10 DOI: 10.15330/cmp.15.1.246-259
A. Serdyuk, I. V. Sokolenko
{"title":"Asymptotic estimates for the widths of classes of functions of high smothness","authors":"A. Serdyuk, I. V. Sokolenko","doi":"10.15330/cmp.15.1.246-259","DOIUrl":"https://doi.org/10.15330/cmp.15.1.246-259","url":null,"abstract":"We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2pi$-periodic functions $varphi$, such that $|varphi|_2le1$, with fixed generated kernels $Psi_{bar{beta}}$, which have Fourier series of the form $$sumlimits_{k=1}^infty psi(k)cos(kt-beta_kpi/2),$$ where $psi(k)ge0,$ $sumpsi^2(k)<infty, beta_kinmathbb{R}$. It is shown that for rapidly decreasing sequences $psi(k)$ (in particular, if $limlimits_{krightarrowinfty}{psi(k+1)}/{psi(k)}=0$) the obtained estimates are asymptotic equalities. We establish that asymptotic equalities for widths of this classes are realized by trigonometric Fourier sums.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74703455","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}
引用次数: 0
Inverse problems of determining an unknown depending on time coefficient for a parabolic equation with involution and periodicity conditions 具有对合和周期性条件的抛物方程随时间系数确定未知数的反问题
IF 0.8
Carpathian Mathematical Publications Pub Date : 2023-03-27 DOI: 10.15330/cmp.15.1.5-19
Y. Baranetskij, I. Demkiv, A. Solomko
{"title":"Inverse problems of determining an unknown depending on time coefficient for a parabolic equation with involution and periodicity conditions","authors":"Y. Baranetskij, I. Demkiv, A. Solomko","doi":"10.15330/cmp.15.1.5-19","DOIUrl":"https://doi.org/10.15330/cmp.15.1.5-19","url":null,"abstract":"The solution of the investigated problem with an unknown coefficient in the equation was constructed by using the method of separation of variables. The properties of the induced spectral problem for the second-order differential equation with involution are studied. The dependence on the equation involutive part of the spectrum and its multiplicity as well as the structure of the system of root functions and partial solutions of the problem were investigated. The conditions for the existence and uniqueness of the solution of the inverse problem have been established. To determine the required coefficient, Volterra's integral equation of the second kind was found and solved.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75811136","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}
引用次数: 0
A new kind of soft algebraic structures: bipolar soft Lie algebras 一类新的软代数结构:双极软李代数
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.464-474
F. Çitak
{"title":"A new kind of soft algebraic structures: bipolar soft Lie algebras","authors":"F. Çitak","doi":"10.15330/cmp.14.2.464-474","DOIUrl":"https://doi.org/10.15330/cmp.14.2.464-474","url":null,"abstract":"In this paper, basic concepts of soft set theory was mentioned. Then, bipolar soft Lie algebra and bipolar soft Lie ideal were defined with the help of soft sets. Some algebraic properties of the new concepts were investigated. The relationship between the two structures were analyzed. Also, it was proved that the level cuts of a bipolar soft Lie algebra were Lie subalgebras of a Lie algebra by the new definitions. After then, soft image and soft preimage of a bipolar soft Lie algebra/ideal were proved to be a bipolar soft Lie algebra/ideal.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73814575","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}
引用次数: 0
Generalized integral type mappings on orthogonal metric spaces 正交度量空间上的广义积分型映射
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.485-492
Ö. Acar, E. Erdoğan, A. S. Özkapu
{"title":"Generalized integral type mappings on orthogonal metric spaces","authors":"Ö. Acar, E. Erdoğan, A. S. Özkapu","doi":"10.15330/cmp.14.2.485-492","DOIUrl":"https://doi.org/10.15330/cmp.14.2.485-492","url":null,"abstract":"This study is devoted to investigate the problem whether the existence and uniqueness of integral type contraction mappings on orthogonal metric spaces. At the end, we give an example to illustrative our main result.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81795648","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}
引用次数: 0
On $ast$-measure monads on the category of ultrametric spaces 关于超度量空间范畴上的$ast$-measure单子
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.429-436
Kh.O. Sukhorukova, M. Zarichnyǐ
{"title":"On $ast$-measure monads on the category of ultrametric spaces","authors":"Kh.O. Sukhorukova, M. Zarichnyǐ","doi":"10.15330/cmp.14.2.429-436","DOIUrl":"https://doi.org/10.15330/cmp.14.2.429-436","url":null,"abstract":"The functor of $ast$-measures of compact support on the category of ultrametric spaces and non-expanding maps is introduced in the previous publication of the authors. In the present note, we prove that this functor determines a monad on this category. The monad structure allows us to define the tensor product of $ast$-measures. We consider some applications of this notion to equilibrium theory.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79492525","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}
引用次数: 1
Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion 弱扩散抛物型微分方程系统中行波的存在性与稳定性
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.493-503
I. Klevchuk
{"title":"Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion","authors":"I. Klevchuk","doi":"10.15330/cmp.14.2.493-503","DOIUrl":"https://doi.org/10.15330/cmp.14.2.493-503","url":null,"abstract":"The aim of the present paper is to investigate of some properties of periodic solutions of a nonlinear autonomous parabolic systems with a periodic condition. We investigate parabolic systems of differential equations using an integral manifolds method of the theory of nonlinear oscillations. We prove the existence of periodic solutions in an autonomous parabolic system of differential equations with weak diffusion on the circle. We study the existence and stability of an arbitrarily large finite number of cycles for a parabolic system with weak diffusion. The periodic solution of parabolic equation is sought in the form of traveling wave. A representation of the integral manifold is obtained. We seek a solution of parabolic system with the periodic condition in the form of a Fourier series in the complex form and introduce a norm in the space of the coefficients in the Fourier expansion. We use the normal forms method in the general parabolic system of differential equations with retarded argument and weak diffusion. We use bifurcation theory for delay differential equations and quasilinear parabolic equations. The existence of periodic solutions in an autonomous parabolic system of differential equations on the circle with retarded argument and small diffusion is proved. The problems of existence and stability of traveling waves in the parabolic system with retarded argument and weak diffusion are investigated.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90122018","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}
引用次数: 0
Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals 基于新Katugampola广义分数积分的Hermite-Hadamard型广义分数不等式
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.475-484
M. Omaba
{"title":"Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals","authors":"M. Omaba","doi":"10.15330/cmp.14.2.475-484","DOIUrl":"https://doi.org/10.15330/cmp.14.2.475-484","url":null,"abstract":"A new generalization of the Katugampola generalized fractional integrals in terms of the Mittag-Leffler functions is proposed. Consequently, new generalizations of the Hermite-Hadamard inequalities by this newly proposed fractional integral operator, for a positive convex stochastic process, are established. Other known results are easily deduced as particular cases of these inequalities. The obtained results also hold for any convex function.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80013707","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}
引用次数: 0
On $A$-statistical convergence and $A$-statistical Cauchy via idea 基于思想的$A$统计收敛与$A$统计柯西
IF 0.8
Carpathian Mathematical Publications Pub Date : 2022-12-30 DOI: 10.15330/cmp.14.2.442-452
O. H. Edely, M. Mursaleen
{"title":"On $A$-statistical convergence and $A$-statistical Cauchy via idea","authors":"O. H. Edely, M. Mursaleen","doi":"10.15330/cmp.14.2.442-452","DOIUrl":"https://doi.org/10.15330/cmp.14.2.442-452","url":null,"abstract":"In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$-  and $A^{I^{ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$-  and $A^{I^{ast }}$-statistical convergence.","PeriodicalId":42912,"journal":{"name":"Carpathian Mathematical Publications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73314077","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}
引用次数: 0
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