: In this work, complete Lyapunov functionals (LFs) are constructed and used for the established conditions on the nonlinear functions appearing in the main equation, to guarantee stochastically asymptotically stable (SAS), uniformly stochastically bounded (USB) and uniformly exponentially asymptotically stable (UEAS) in probability of solutions to the nonautonomous third-order stochastic differential equation (SDE) with a constant delay as ... x ( t ) + a ( t ) f ( x ( t ) , ˙ x ( t ))¨ x ( t ) + b ( t ) φ (
{"title":"On the properties of solutions for nonautonomous third-order stochastic differential equation with a constant delay","authors":"A. Mahmoud, D. Bakhit","doi":"10.55730/1300-0098.3351","DOIUrl":"https://doi.org/10.55730/1300-0098.3351","url":null,"abstract":": In this work, complete Lyapunov functionals (LFs) are constructed and used for the established conditions on the nonlinear functions appearing in the main equation, to guarantee stochastically asymptotically stable (SAS), uniformly stochastically bounded (USB) and uniformly exponentially asymptotically stable (UEAS) in probability of solutions to the nonautonomous third-order stochastic differential equation (SDE) with a constant delay as ... x ( t ) + a ( t ) f ( x ( t ) , ˙ x ( t ))¨ x ( t ) + b ( t ) φ (","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44442654","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}
: In this paper, we state and prove theorems related to the existence and multiplicity for positive solutions of a system of first order differential equations with multipoint and integral boundary conditions. The main tool is the fixed point theory. In order to illustrate the main results, we present some examples.
{"title":"Existence and multiplicity for positive solutions of a system of first order differential equations with multipoint and integral boundary conditions","authors":"L. Ngoc, N. Long","doi":"10.55730/1300-0098.3352","DOIUrl":"https://doi.org/10.55730/1300-0098.3352","url":null,"abstract":": In this paper, we state and prove theorems related to the existence and multiplicity for positive solutions of a system of first order differential equations with multipoint and integral boundary conditions. The main tool is the fixed point theory. In order to illustrate the main results, we present some examples.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43804967","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}
Hali̇t Taş, Yelda Aygar Küçükevcilioğlu, Elgiz Bayram
: In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example
{"title":"Scattering solutions and scattering function of a Klein-Gordon s-wave equation with jump conditions","authors":"Hali̇t Taş, Yelda Aygar Küçükevcilioğlu, Elgiz Bayram","doi":"10.55730/1300-0098.3390","DOIUrl":"https://doi.org/10.55730/1300-0098.3390","url":null,"abstract":": In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43863084","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}
: In a ring with an involution, we first present some necessary and sufficient conditions for the existence of the m -weak group inverse and expression. As an application, we prove that a regular element a is ( m + 1) -weak group invertible if and only if a 2 a − is m -weak group invertible, where a − is an inner inverse of a . The relevant results for weak core inverses and for pseudocore inverses are given. In addition, we present some new characterizations of weak core inverses, and also investigate maximal classes of elements determining weak core inverses.
{"title":"Characterizations and representations of weak core inverses and $m$-weak group inverses","authors":"Wende Li, Jianlong Chen, Yukun Zhou","doi":"10.55730/1300-0098.3440","DOIUrl":"https://doi.org/10.55730/1300-0098.3440","url":null,"abstract":": In a ring with an involution, we first present some necessary and sufficient conditions for the existence of the m -weak group inverse and expression. As an application, we prove that a regular element a is ( m + 1) -weak group invertible if and only if a 2 a − is m -weak group invertible, where a − is an inner inverse of a . The relevant results for weak core inverses and for pseudocore inverses are given. In addition, we present some new characterizations of weak core inverses, and also investigate maximal classes of elements determining weak core inverses.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41384803","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}
: In this note, we provide an example to illustrate that Proposition 2.4 in [Turkish Journal of Mathematics (2021)45: 955-960)] is incorrect, and give a modification of the proposition. Two examples are provided to illustrate the modified result. Meanwhile, we establish a convex function, and correct the proof of Theorem 2.3 in [Turkish Journal of Mathematics (2021)45: 955-960)] by the function.
{"title":"A note on \"Some properties of second-order weak subdifferentials\" [Turkish Journal of Mathematics (2021)45: 955-960]","authors":"Qilin Wang, Min Liu","doi":"10.55730/1300-0098.3358","DOIUrl":"https://doi.org/10.55730/1300-0098.3358","url":null,"abstract":": In this note, we provide an example to illustrate that Proposition 2.4 in [Turkish Journal of Mathematics (2021)45: 955-960)] is incorrect, and give a modification of the proposition. Two examples are provided to illustrate the modified result. Meanwhile, we establish a convex function, and correct the proof of Theorem 2.3 in [Turkish Journal of Mathematics (2021)45: 955-960)] by the function.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45424117","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}
: This paper establishes an identity for the case of differentiable s − convex functions with respect to the conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by s − convex functions with the help of the conformable fractional integrals. Several important inequalities are acquired with taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Moreover, an example using graph is given in order to show that our main results are correct. By using the special choices of the obtained results, we present several new results connected with trapezoid-type inequalities.
{"title":"Novel results on trapezoid-type inequalities for conformable fractional integrals","authors":"F. Hezenci, H. Budak","doi":"10.55730/1300-0098.3371","DOIUrl":"https://doi.org/10.55730/1300-0098.3371","url":null,"abstract":": This paper establishes an identity for the case of differentiable s − convex functions with respect to the conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by s − convex functions with the help of the conformable fractional integrals. Several important inequalities are acquired with taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Moreover, an example using graph is given in order to show that our main results are correct. By using the special choices of the obtained results, we present several new results connected with trapezoid-type inequalities.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45482052","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}
M. B. D. Ngaha, Salomon Joseph Mbatakou, Romain Nimpa Pefoukeu
: In this paper, Szabó’s algorithm is used as the main tool to find locally symmetric left invariant Riemannian metrics on some 4 -dimensional Lie groups. Locally symmetric left invariant Riemannian Lie groups constitute an important subclass of Riemannian Lie groups with zero-divergence Weyl-tensor the so-called C-manifolds. Some properties of the curvature operator of these 4-dimensional C-manifolds are studied.
{"title":"Szabos algorithm and applications","authors":"M. B. D. Ngaha, Salomon Joseph Mbatakou, Romain Nimpa Pefoukeu","doi":"10.55730/1300-0098.3419","DOIUrl":"https://doi.org/10.55730/1300-0098.3419","url":null,"abstract":": In this paper, Szabó’s algorithm is used as the main tool to find locally symmetric left invariant Riemannian metrics on some 4 -dimensional Lie groups. Locally symmetric left invariant Riemannian Lie groups constitute an important subclass of Riemannian Lie groups with zero-divergence Weyl-tensor the so-called C-manifolds. Some properties of the curvature operator of these 4-dimensional C-manifolds are studied.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45571953","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}
: In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curves is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Caputo fractional analysis that fits the algebraic structure of differential geometry is used. This is because the Caputo fractional derivative of the constant function is zero. This is an important advantage and allows a variety of fractional physical problems to be based on a geometric basis. This effect is examined with the help of examples consistent with the theory and visualized for different values of the Caputo fractional analysis. The difference of this study from others is the use of Caputo fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics, signal processing, etc. Fractional derivatives and integrals have become extremely important as they give more numerical results than classical solutions in solving various problems in many fields. In addition, many problems that cannot be answered by classical analysis have been solved by Caputo fractional analysis. In this context, the curvatures of a curve are calculated by Caputo fractional analysis and obtained differently from the classical result. It is aimed to characterize the curve more accurately with the numerically more accurate calculation of the curvatures.
{"title":"Effect of fractional analysis on some special curves","authors":"Aykut Has, B. Yilmaz","doi":"10.55730/1300-0098.3438","DOIUrl":"https://doi.org/10.55730/1300-0098.3438","url":null,"abstract":": In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curves is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Caputo fractional analysis that fits the algebraic structure of differential geometry is used. This is because the Caputo fractional derivative of the constant function is zero. This is an important advantage and allows a variety of fractional physical problems to be based on a geometric basis. This effect is examined with the help of examples consistent with the theory and visualized for different values of the Caputo fractional analysis. The difference of this study from others is the use of Caputo fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics, signal processing, etc. Fractional derivatives and integrals have become extremely important as they give more numerical results than classical solutions in solving various problems in many fields. In addition, many problems that cannot be answered by classical analysis have been solved by Caputo fractional analysis. In this context, the curvatures of a curve are calculated by Caputo fractional analysis and obtained differently from the classical result. It is aimed to characterize the curve more accurately with the numerically more accurate calculation of the curvatures.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48245687","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}
: This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the p -adic Volkenborn integral to the Catalan-type polynomials, some combinatorial sums and identities involving the Bernoulli numbers, the Stirling numbers and the Catalan-type numbers are derived.
{"title":"Generating functions for reciprocal Catalan-type sums: approach to linear differentiation equation and ($p$-adic) integral equations","authors":"Damla Gün, Yilmaz Simsek","doi":"10.55730/1300-0098.3396","DOIUrl":"https://doi.org/10.55730/1300-0098.3396","url":null,"abstract":": This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the p -adic Volkenborn integral to the Catalan-type polynomials, some combinatorial sums and identities involving the Bernoulli numbers, the Stirling numbers and the Catalan-type numbers are derived.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43893427","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}
: We prove that Bergman projections on weighted mixed norm spaces on smoothly bounded domains in R n are bounded for a certain range of parameters of such spaces and assuming certain conditions on weights. The proof relies on estimates of integral means of M p ( P γ f, r ) in terms of integral means of f . This result complements earlier result on boundedness of P γ on a closely related space L p,qα (Ω)
{"title":"Boundedness of Bergman projections acting on weighted mixed norm spaces","authors":"Ivana Savković","doi":"10.55730/1300-0098.3387","DOIUrl":"https://doi.org/10.55730/1300-0098.3387","url":null,"abstract":": We prove that Bergman projections on weighted mixed norm spaces on smoothly bounded domains in R n are bounded for a certain range of parameters of such spaces and assuming certain conditions on weights. The proof relies on estimates of integral means of M p ( P γ f, r ) in terms of integral means of f . This result complements earlier result on boundedness of P γ on a closely related space L p,qα (Ω)","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42093079","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}
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