Pub Date : 2021-02-01DOI: 10.22130/SCMA.2020.121704.751
H. Fard, Mohammad Ali
The duals of Gabor frames have an essential role in reconstruction of signals. In this paper we find a necessary and sufficient condition for two Gabor systems $left(chi_{left[c_1,d_1right)},a,bright)$ and $left(chi_{left[c_2,d_2right)},a,bright)$ to form dual frames for $L_2left(mathbb{R}right)$, where $a$ and $b$ are positive numbers and $c_1,c_2,d_1$ and $d_2$ are real numbers such that $c_1
{"title":"Gabor Dual Frames with Characteristic Function Window","authors":"H. Fard, Mohammad Ali","doi":"10.22130/SCMA.2020.121704.751","DOIUrl":"https://doi.org/10.22130/SCMA.2020.121704.751","url":null,"abstract":"The duals of Gabor frames have an essential role in reconstruction of signals. In this paper we find a necessary and sufficient condition for two Gabor systems $left(chi_{left[c_1,d_1right)},a,bright)$ and $left(chi_{left[c_2,d_2right)},a,bright)$ to form dual frames for $L_2left(mathbb{R}right)$, where $a$ and $b$ are positive numbers and $c_1,c_2,d_1$ and $d_2$ are real numbers such that $c_1","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"47-57"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44849359","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}
Pub Date : 2021-02-01DOI: 10.22130/SCMA.2020.120323.739
Seshagiri Rao, K. Kalyani
The aim of this paper is to prove some coupled fixed point theorems of a self mapping satisfying a certain rational type contraction along with strict mixed monotone property in an ordered metric space. Further, a result is presented for the uniqueness of a coupled fixed point under an order relation in a space. These results generalize and extend known existing results in the literature.
{"title":"On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces","authors":"Seshagiri Rao, K. Kalyani","doi":"10.22130/SCMA.2020.120323.739","DOIUrl":"https://doi.org/10.22130/SCMA.2020.120323.739","url":null,"abstract":"The aim of this paper is to prove some coupled fixed point theorems of a self mapping satisfying a certain rational type contraction along with strict mixed monotone property in an ordered metric space. Further, a result is presented for the uniqueness of a coupled fixed point under an order relation in a space. These results generalize and extend known existing results in the literature.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"123-136"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41961053","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}
Pub Date : 2020-12-27DOI: 10.22130/SCMA.2020.127223.795
A. Zivari-kazempour, M. Valaei
For Banach algebras $mathcal{A}$ and $mathcal{B}$, we show that if $mathfrak{A}=mathcal{A}times mathcal{B}$ is unital, then each bi-multiplicative mapping from $mathfrak{A}$ into a semisimple commutative Banach algebra $mathcal{D}$ is jointly continuous. This conclusion generalizes a famous result due to$check{text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-multiplicative functionals on $mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$.
{"title":"Joint Continuity of Bi-multiplicative Functionals","authors":"A. Zivari-kazempour, M. Valaei","doi":"10.22130/SCMA.2020.127223.795","DOIUrl":"https://doi.org/10.22130/SCMA.2020.127223.795","url":null,"abstract":"For Banach algebras $mathcal{A}$ and $mathcal{B}$, we show that if $mathfrak{A}=mathcal{A}times mathcal{B}$ is unital, then each bi-multiplicative mapping from $mathfrak{A}$ into a semisimple commutative Banach algebra $mathcal{D}$ is jointly continuous. This conclusion generalizes a famous result due to$check{text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-multiplicative functionals on $mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48352376","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}
Pub Date : 2020-12-06DOI: 10.22130/SCMA.2020.122380.764
G. Haghighatdoost, S. Abdolhadi-zangakani, Rasoul Mahjoubi-Bahman
In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix for this family of bi-Hamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.
{"title":"Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups","authors":"G. Haghighatdoost, S. Abdolhadi-zangakani, Rasoul Mahjoubi-Bahman","doi":"10.22130/SCMA.2020.122380.764","DOIUrl":"https://doi.org/10.22130/SCMA.2020.122380.764","url":null,"abstract":"In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix for this family of bi-Hamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"89-105"},"PeriodicalIF":0.0,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43331469","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}
Pub Date : 2020-12-06DOI: 10.22130/SCMA.2020.121963.759
H. Budak, Ebru Pehlivan, Pınar Kosem
In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{prime }(a+b-x)geq f^{prime }(x)$ for all $xin left[ a,frac{a+b}{2}right] $ instead of convexity.
{"title":"On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals","authors":"H. Budak, Ebru Pehlivan, Pınar Kosem","doi":"10.22130/SCMA.2020.121963.759","DOIUrl":"https://doi.org/10.22130/SCMA.2020.121963.759","url":null,"abstract":"In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{prime }(a+b-x)geq f^{prime }(x)$ for all $xin left[ a,frac{a+b}{2}right] $ instead of convexity.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"73-88"},"PeriodicalIF":0.0,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41769364","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}
Pub Date : 2020-11-21DOI: 10.22130/SCMA.2020.130958.827
Ahmad Ahmdi, A. Rahimi
Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define the $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.
{"title":"$K$-orthonormal and $K$-Riesz Bases","authors":"Ahmad Ahmdi, A. Rahimi","doi":"10.22130/SCMA.2020.130958.827","DOIUrl":"https://doi.org/10.22130/SCMA.2020.130958.827","url":null,"abstract":"Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define the $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"59-72"},"PeriodicalIF":0.0,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47342058","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}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.127585.801
A. Najati, B. Noori, M. B. Moghimi
In this paper, we have improved some of the results in [C. Choi and B. Lee, Stability of Mixed Additive-Quadratic and Additive--Drygas Functional Equations. Results Math. 75 no. 1 (2020), Paper No. 38]. Indeed, we investigate the Hyers-Ulam stability problem of the following functional equationsbegin{align*} 2varphi(x + y) + varphi(x - y) &= 3varphi(x)+ 3varphi(y) 2psi(x + y) + psi(x - y) &= 3psi(x) + 2psi(y) + psi(-y).end{align*}We also consider the Pexider type functional equation [2psi(x + y) + psi(x - y) = f(x) + g(y),] and the additive functional equation[2psi(x + y) + psi(x - y) = 3psi(x) + psi(y).]
{"title":"On the Stability of Mixed Additive--Quadratic and Additive--Drygas Functional Equations","authors":"A. Najati, B. Noori, M. B. Moghimi","doi":"10.22130/SCMA.2020.127585.801","DOIUrl":"https://doi.org/10.22130/SCMA.2020.127585.801","url":null,"abstract":"In this paper, we have improved some of the results in [C. Choi and B. Lee, Stability of Mixed Additive-Quadratic and Additive--Drygas Functional Equations. Results Math. 75 no. 1 (2020), Paper No. 38]. Indeed, we investigate the Hyers-Ulam stability problem of the following functional equationsbegin{align*} 2varphi(x + y) + varphi(x - y) &= 3varphi(x)+ 3varphi(y) 2psi(x + y) + psi(x - y) &= 3psi(x) + 2psi(y) + psi(-y).end{align*}We also consider the Pexider type functional equation [2psi(x + y) + psi(x - y) = f(x) + g(y),] and the additive functional equation[2psi(x + y) + psi(x - y) = 3psi(x) + psi(y).]","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"18 1","pages":"35-46"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46836009","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}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.118420.722
Nurcan Bilgili Gungor, D. Turkoglu
In this paper, some fixed point results of self mapping which is defined on orthogonal cone metric spaces are given by using extensions of orthogonal contractions. And by taking advantage of these results, the necessary conditions for self mappings on orthogonal cone metric space to have P property are investigated. Also an example is given to illustrate the main results.
{"title":"Fixed Point Results for Extensions of Orthogonal Contraction on Orthogonal Cone Metric Space","authors":"Nurcan Bilgili Gungor, D. Turkoglu","doi":"10.22130/SCMA.2020.118420.722","DOIUrl":"https://doi.org/10.22130/SCMA.2020.118420.722","url":null,"abstract":"In this paper, some fixed point results of self mapping which is defined on orthogonal cone metric spaces are given by using extensions of orthogonal contractions. And by taking advantage of these results, the necessary conditions for self mappings on orthogonal cone metric space to have P property are investigated. Also an example is given to illustrate the main results.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"95-107"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44622362","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}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.119707.736
Faride Ghorbani Moghaddam, A. Z. Bahabadi, B. Honary
In this paper, we introduce chaotic measure for discrete and continuous dynamical systems and study some properties of measure chaotic systems. Also relationship between chaotic measure, ergodic and expansive measures is investigated. Finally, we prove a new version of variational principle for chaotic measure.
{"title":"On Measure Chaotic Dynamical Systems","authors":"Faride Ghorbani Moghaddam, A. Z. Bahabadi, B. Honary","doi":"10.22130/SCMA.2020.119707.736","DOIUrl":"https://doi.org/10.22130/SCMA.2020.119707.736","url":null,"abstract":"In this paper, we introduce chaotic measure for discrete and continuous dynamical systems and study some properties of measure chaotic systems. Also relationship between chaotic measure, ergodic and expansive measures is investigated. Finally, we prove a new version of variational principle for chaotic measure.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"25-37"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43676571","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}
Pub Date : 2020-11-01DOI: 10.22130/SCMA.2020.118014.720
K. Noor, Shujaat Ali Shah
Let $f$ and $g$ be analytic in the open unit disc and, for $alpha ,$ $beta geq 0$, letbegin{align*}Jleft( alpha ,beta ,f,gright) & =frac{zf^{prime }(z)}{f^{1-alpha}(z)g^{alpha }(z)}+beta left( 1+frac{zf^{prime prime }(z)}{f^{prime}(z)}right) -beta left( 1-alpha right) frac{zf^{prime }(z)}{f(z)} & quad -alpha beta frac{zg^{prime }(z)}{g(z)}text{.}end{align*}The main aim of this paper is to study the class of analytic functions which map $Jleft( alpha ,beta ,f,gright) $ onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.
{"title":"On Certain Generalized Bazilevic type Functions Associated with Conic Regions","authors":"K. Noor, Shujaat Ali Shah","doi":"10.22130/SCMA.2020.118014.720","DOIUrl":"https://doi.org/10.22130/SCMA.2020.118014.720","url":null,"abstract":"Let $f$ and $g$ be analytic in the open unit disc and, for $alpha ,$ $beta geq 0$, letbegin{align*}Jleft( alpha ,beta ,f,gright) & =frac{zf^{prime }(z)}{f^{1-alpha}(z)g^{alpha }(z)}+beta left( 1+frac{zf^{prime prime }(z)}{f^{prime}(z)}right) -beta left( 1-alpha right) frac{zf^{prime }(z)}{f(z)} & quad -alpha beta frac{zg^{prime }(z)}{g(z)}text{.}end{align*}The main aim of this paper is to study the class of analytic functions which map $Jleft( alpha ,beta ,f,gright) $ onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"13-23"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43131095","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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