Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a $K^*$-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.
{"title":"New aspects of weaving K-frames: the excess and duality","authors":"Elahe AGHESHTEH MOGHADDAM, A. Arefijamaal","doi":"10.15672/hujms.1008448","DOIUrl":"https://doi.org/10.15672/hujms.1008448","url":null,"abstract":"Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K.\u0000In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames.\u0000Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a $K^*$-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82431208","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 establish the concept of compact operators defined between Riesz spaces with respect to statistical order convergence. An operator mapping any statistical order bounded sequence to a sequence with a statistical order convergent subsequence between Riesz spaces is called statistical order compact. Moreover, we also define the notion of statistical M-weakly compact operators. By applying these nontopological concepts, we obtain some new results about these operators.
{"title":"Statistically order compact operators on Riesz spaces","authors":"Abdullah Aydin","doi":"10.15672/hujms.1223922","DOIUrl":"https://doi.org/10.15672/hujms.1223922","url":null,"abstract":"In this paper, we state and establish the concept of compact operators defined between Riesz spaces with respect to statistical order convergence. An operator mapping any statistical order bounded sequence to a sequence with a statistical order convergent subsequence between Riesz spaces is called statistical order compact. Moreover, we also define the notion of statistical M-weakly compact operators. By applying these nontopological concepts, we obtain some new results about these operators.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"13 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87243840","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 present a new and efficient algorithm to compute affine equivalences and symmetries between two trigonometric curves in an arbitrary dimension. The algorithm benefits from the power of invariance and polynomial gcd and factoring without solving any system of equations. The algorithm is implemented in MAPLE, and extensive experimentations demonstrating the efficiency of the method are given.
{"title":"Computing affine equivalences and symmetries of trigonometric curves in arbitrary dimension","authors":"Uğur Gözütok","doi":"10.15672/hujms.1277665","DOIUrl":"https://doi.org/10.15672/hujms.1277665","url":null,"abstract":"We present a new and efficient algorithm to compute affine equivalences and symmetries between two trigonometric curves in an arbitrary dimension. The algorithm benefits from the power of invariance and polynomial gcd and factoring without solving any system of equations. The algorithm is implemented in MAPLE, and extensive experimentations demonstrating the efficiency of the method are given.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80854803","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}
Gel'fand Dorfman superbialgebra, which is both a Lie superalgebra and a (left) Novikov superalgebra with some compatibility condition, appears in the study of Hamiltonian pairs in completely integrable systems and a class of special Lie conformal superalgebras called quadratic Lie conformal superalgebras. In the present paper, we generalize this algebraic structure to the Hom-conformal case . We introduce first, Hom-Novikov conformal superalgebras and exihibit several properties. Then we introduce Hom-Gel'fand Dorfman superbialgebra and provide some construction results.
Gel’fand Dorfman超双代数是一个李超代数和一个具有相容条件的(左)Novikov超代数，它出现在研究完全可积系统中的哈密顿对和一类特殊的李共形超代数——二次李共形超代数中。在本文中，我们将这种代数结构推广到homo -共形情况。首先，我们引入了homn - novikov共形超代数，并证明了几个性质。然后引入了homg - gel 'fand Dorfman超双代数，并给出了一些构造结果。
{"title":"Hom-Gel'fand-Dorfman conformal superbialgebras","authors":"Taoufik Chti̇oui̇","doi":"10.15672/hujms.1196147","DOIUrl":"https://doi.org/10.15672/hujms.1196147","url":null,"abstract":"Gel'fand Dorfman superbialgebra, which is both a Lie superalgebra and a\u0000(left) Novikov superalgebra with some compatibility condition, appears in the study of\u0000Hamiltonian pairs in completely integrable systems and a class of special Lie\u0000conformal superalgebras called quadratic Lie conformal superalgebras. In the present paper, we generalize this algebraic structure to the Hom-conformal case . We introduce first, Hom-Novikov conformal superalgebras and exihibit several properties. Then we introduce Hom-Gel'fand Dorfman superbialgebra and provide some construction results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77635165","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 study composition-differentiation operators acting on the Bergman and Dirichlet space of the unit disk. We first characterize the compactness of this operator on weighted Bergman spaces. We shall then prove that for an analytic self-map $varphi$ on the unit disk $disk$, the induced composition-differentiation operator is bounded with dense range if and only if $varphi$ is univalent and the polynomials are dense in the Bergman space on $varphi(disk)$.
{"title":"Composition-differentiation operators acting on certain Hilbert spaces of analytic functions","authors":"Yazdan Bayat, A. Abkar","doi":"10.15672/hujms.1241783","DOIUrl":"https://doi.org/10.15672/hujms.1241783","url":null,"abstract":"We study composition-differentiation operators acting on the Bergman and Dirichlet space of the unit disk. We first characterize the compactness of this operator on weighted Bergman spaces. We shall then prove that for an analytic self-map $varphi$ on the unit disk $disk$, the induced composition-differentiation operator is bounded with dense range if and only if $varphi$ is univalent and the polynomials are dense in the Bergman space on $varphi(disk)$.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"48 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75319294","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}
D. Gopal, N. Özgür, Jayesh Savali̇ya, S. K. Srivastava
Geometric approaches are important for the study of some real-life problems. In metric fixed point theory, a recent problem called textquotedblleft textit{fixed-figure problem}textquotedblright is the investigation of the existence of self-mapping which remain invariant at each points of a certain geometric figure (e.g. a circle, an ellipse and a Cassini curve) in the space. This problem is well studied in the domain of the extension of this line of research in the context of fixed circle, fixed disc, fixed ellipse, fixed Cassini curve and so on. In this paper, we introduce the concept of a Suzuki type $mathcal{Z}_c$-contraction. We deal with the fixed-figure problem by means of the notions of a $mathcal{Z}_c$-contraction and a Suzuki type $mathcal{Z}_c$-contraction. We derive new fixed-figure results for the fixed ellipse and fixed Cassini curve cases by means of these notions. Also fixed disc and fixed circle results given for Suzuki type $mathcal{Z}_c$-contraction. There are couple of illustration related to the obtained theoretical results.
{"title":"Suzuki type $mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem","authors":"D. Gopal, N. Özgür, Jayesh Savali̇ya, S. K. Srivastava","doi":"10.15672/hujms.1287530","DOIUrl":"https://doi.org/10.15672/hujms.1287530","url":null,"abstract":"Geometric approaches are important for the study of some real-life problems. In metric fixed point theory, a recent problem called textquotedblleft textit{fixed-figure problem}textquotedblright is the investigation of the existence of self-mapping which remain invariant at each points of a certain geometric figure (e.g. a circle, an ellipse and a Cassini curve) in the space. This problem is well studied in the domain of the extension of this line of research in the context of fixed circle, fixed disc, fixed ellipse, fixed Cassini curve and so on. In this paper, we introduce the concept of a Suzuki type $mathcal{Z}_c$-contraction. We deal with the fixed-figure problem by means of the notions of a $mathcal{Z}_c$-contraction and a Suzuki type $mathcal{Z}_c$-contraction. We derive new fixed-figure results for the fixed ellipse and fixed Cassini curve cases by means of these notions. Also fixed disc and fixed circle results given for Suzuki type $mathcal{Z}_c$-contraction. There are couple of illustration related to the obtained theoretical results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"47 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81603130","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, three natural fuzzifying topologies are presented on the fuzzy real line. Then the notion of fuzzifying pseudo-quasi-metrics is introduced. It is proved that the three fuzzifying topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. Our definition of fuzzifying pseudo-metric is slightly different from that of KM-fuzzy metric. A fuzzifying pseudo-metrics can be regarded as a weak form of a KM fuzzy metric.
{"title":"Fuzzifying pseudo-metric topologies on the fuzzy real line","authors":"F. Shi̇","doi":"10.15672/hujms.1209995","DOIUrl":"https://doi.org/10.15672/hujms.1209995","url":null,"abstract":"In this paper, three natural fuzzifying topologies are presented on the fuzzy real line. Then the notion of fuzzifying pseudo-quasi-metrics is introduced. It is proved that the three fuzzifying topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. Our definition of fuzzifying pseudo-metric is slightly different from that of KM-fuzzy metric. A fuzzifying pseudo-metrics can be regarded as a weak form of a KM fuzzy metric.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"11 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85906377","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}
Let $(X,d,mu)$ be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that bilinear Calder'{o}n-Zygmund operators are bounded from the product of variable exponent Lebesgue spaces $L^{p_{1}(cdot)}(X)times L^{p_{2}(cdot)}(X)$ into spaces $L^{p(cdot)}(X)$, and bounded from product of variable exponent generalized Morrey spaces $mathcal{L}^{p_{1}(cdot),varphi_{1}}(X)times mathcal{L}^{p_{2}(cdot),varphi_{2}}(X)$ into spaces $mathcal{L}^{p(cdot),varphi}(X)$, where the Lebesgue measure functions $varphi(cdot,cdot), varphi_{1}(cdot,cdot)$ and $varphi_{2}(cdot,cdot)$ satisfy $varphi_{1}timesvarphi_{2}=varphi$, and $frac{1}{p(cdot)}=frac{1}{p_{1}(cdot)}+frac{1}{p_{2}(cdot)}$. Furthermore, by establishing sharp maximal estimate for the commutator $[b_{1},b_{2},BT]$ generated by $b_{1}, b_{2}inmathrm{BMO}(X)$ and the $BT$, the author shows that the $[b_{1},b_{2},BT]$ is bounded from product of spaces $L^{p_{1}(cdot)}(X)times L^{p_{2}(cdot)}(X)$ into spaces $L^{p(cdot)}(X)$, and also bounded from product of spaces $mathcal{L}^{p_{1}(cdot),varphi_{1}}(X)times mathcal{L}^{p_{2}(cdot),varphi_{2}}(X)$ into spaces $L^{p(cdot),varphi}(X)$.
{"title":"Estimate for bilinear Calder'{o}n-Zygmund operator and its commutator on homogeneous variable exponent spaces","authors":"G. Lu","doi":"10.15672/hujms.1195476","DOIUrl":"https://doi.org/10.15672/hujms.1195476","url":null,"abstract":"Let $(X,d,mu)$ be a space of homogeneous type in the sense of Coifman and and Weiss. In this setting, the author proves that bilinear Calder'{o}n-Zygmund operators are bounded from the product of variable exponent Lebesgue spaces $L^{p_{1}(cdot)}(X)times L^{p_{2}(cdot)}(X)$ into spaces $L^{p(cdot)}(X)$, and bounded from product of variable exponent generalized Morrey spaces $mathcal{L}^{p_{1}(cdot),varphi_{1}}(X)times mathcal{L}^{p_{2}(cdot),varphi_{2}}(X)$ into spaces $mathcal{L}^{p(cdot),varphi}(X)$, where the Lebesgue measure functions $varphi(cdot,cdot), varphi_{1}(cdot,cdot)$ and $varphi_{2}(cdot,cdot)$ satisfy $varphi_{1}timesvarphi_{2}=varphi$, and $frac{1}{p(cdot)}=frac{1}{p_{1}(cdot)}+frac{1}{p_{2}(cdot)}$. Furthermore, by establishing sharp maximal estimate for the commutator $[b_{1},b_{2},BT]$ generated by $b_{1}, b_{2}inmathrm{BMO}(X)$ and the $BT$, the author shows that the $[b_{1},b_{2},BT]$ is bounded from product of spaces $L^{p_{1}(cdot)}(X)times L^{p_{2}(cdot)}(X)$ into spaces $L^{p(cdot)}(X)$, and also bounded from product of spaces $mathcal{L}^{p_{1}(cdot),varphi_{1}}(X)times mathcal{L}^{p_{2}(cdot),varphi_{2}}(X)$ into spaces $L^{p(cdot),varphi}(X)$.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"129 3 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79601926","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, the concept of the $(p,h)$-convex function is introduced, which generalizes the $p$-convex function and the $h$-convex function, and Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $mathbb{R}^n$ are established. Furthermore, some mappings related to the above inequalities are studied and some known results are generalized.
{"title":"Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $mathbb{R}^n$","authors":"Jianmiao Ruan","doi":"10.15672/hujms.1283922","DOIUrl":"https://doi.org/10.15672/hujms.1283922","url":null,"abstract":"In this paper, the concept of the $(p,h)$-convex function is introduced, which generalizes the $p$-convex function and the $h$-convex function, and Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $mathbb{R}^n$ are established. Furthermore, some mappings related to the above inequalities are studied and some known results are generalized.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"98 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82341156","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 the present work, we introduce the nth-Order subfractional Brownian motion (S_H^n (t), t ≥ 0) with Hurst index H ∈ (n − 1,n) and order n ≥ 1; then we examine some of its basic properties: self-similarity, long-range dependence, non Markovian nature and semimartingale property. A local law of iterated logarithm for S_H^n (t) is also established.
{"title":"On the nth-order subfractional Brownian motion","authors":"E. Mohamed, Mabdaoui Mohamed","doi":"10.15672/hujms.1180888","DOIUrl":"https://doi.org/10.15672/hujms.1180888","url":null,"abstract":"In the present work, we introduce the nth-Order subfractional Brownian motion (S_H^n (t), t ≥ 0) with Hurst index H ∈ (n − 1,n) and order n ≥ 1; then we examine some\u0000of its basic properties: self-similarity, long-range dependence, non Markovian nature and semimartingale property. A local law of iterated logarithm for S_H^n (t) is also established.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"186 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83450026","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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