University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
Some Properties of Lebesgue Fuzzy Metric Spaces
1
14
EN
Sugata
Adhya
0000000171065707
Department of Mathematics, The Bhawanipur Education Society College. 5, Lala Lajpat Rai Sarani, Kolkata 700020, West Bengal, India.
sugataadhya@yahoo.com
Atasi
Deb Ray
0000000273800928
Department of Pure Mathematics, University of Calcutta. 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India.
atasi@hotmail.com
10.22130/scma.2020.120854.743
In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak $G$complete and compact fuzzy metric spaces. We also discuss the Lebesgue property of several wellknown fuzzy metric spaces.
Fuzzy metric space,Lebesgue property,Weak $G$complete
https://scma.maragheh.ac.ir/article_46667.html
https://scma.maragheh.ac.ir/article_46667_f59e7b832de5c1c96be81715fb591613.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
A Note on Some Results for $C$controlled $K$Fusion Frames in Hilbert Spaces
15
34
EN
Habib
Shakoory
Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
habibshakoory@yahoo.com
Reza
Ahmadi
Research Institute for Fundamental Sciences, University of Tabriz, Tabriz, Iran.
rahmadi@tabrizu.ac.ir
Naghi
Behzadi
Research Institute for Fundamental Sciences, University of Tabriz, Tabriz,
Iran.
n.behzadi@tabrizu.ac.ir
Susan
Nami
Faculty of Physic, University of Tabriz, Tabriz, Iran.
s.nami@tabrizu.ac.ir
10.22130/scma.2020.123056.766
In this manuscript, we study the relation between Kfusion frame and its local components which leads to the definition of a $C$controlled $K$fusion frames, also we extend a theory based on Kfusion frames on Hilbert spaces, which prepares exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we define the analysis, synthesis and frame operator for $C$controlled $K$fusion frames, which even yield a reconstruction formula. Also, we define dual of $C$controlled $K$fusion frames and study some basic properties and perturbation of them.
Frame,$k$fusion frame,Controlled fusion frame,Controlled $K$fusion frame
https://scma.maragheh.ac.ir/article_46575.html
https://scma.maragheh.ac.ir/article_46575_1c975979396a5c2cf12c24741735cc21.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
On Approximation of Some Mixed Functional Equations
35
46
EN
Abbas
Najati
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
a.nejati@yahoo.com
Batool
Noori
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
noori.batool@yahoo.com
Mohammad Bagher
Moghimi
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
mbfmoghimi@yahoo.com
10.22130/scma.2020.127585.801
In this paper, we have improved some of the results in [C. Choi and B. Lee, Stability of Mixed AdditiveQuadratic and AdditiveDrygas Functional Equations. Results Math. 75 no. 1 (2020), Paper No. 38]. Indeed, we investigate the HyersUlam stability problem of the following functional equations<br />begin{align*}<br /> 2varphi(x + y) + varphi(x  y) &= 3varphi(x)+ 3varphi(y) \<br /> 2psi(x + y) + psi(x  y) &= 3psi(x) + 2psi(y) + psi(y).<br />end{align*}<br />We also consider the Pexider type functional equation [2psi(x + y) + psi(x  y) = f(x) + g(y),] and the additive functional equation<br />[2psi(x + y) + psi(x  y) = 3psi(x) + psi(y).]
HyersUlam stability,Additive,Quadratic,Drygas,Functional equation,Lebesgue measure zero,Pexider equation
https://scma.maragheh.ac.ir/article_46665.html
https://scma.maragheh.ac.ir/article_46665_3ce38b61e7b850642214401464923acf.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
Gabor Dual Frames with Characteristic Function Window
47
57
EN
Mohammad Ali
Hasankhani Fard
Department of Mathematics, ValieAsr University of Rafsanjan, P.O.Box 546, Rafsanjan, Iran.
m.hasankhani@vru.ac.ir
10.22130/scma.2020.121704.751
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 $c_1<d_1$ and $c_2<d_2$.
Frame,Dual frame,Gabor system,Gabor frame
https://scma.maragheh.ac.ir/article_46666.html
https://scma.maragheh.ac.ir/article_46666_d613662078ce4df44a79d834be6b2f64.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
$K$orthonormal and $K$Riesz Bases
59
72
EN
Ahmad
Ahmdi
0000000198702374
Department of Mathematics, Faculty of Science, University of Hormozgan, P.O.Box 7916193145, Bandar Abbas, Iran.
ahmadi_a@hormozgan.ac.ir
Asghar
Rahimi
0000000320956811
Department of Mathematics, Faculty of Science, University of Maragheh, P.O.Box 55136553, Maragheh, Iran.
rahimi@maragheh.ac.ir
10.22130/scma.2020.130958.827
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.
$K$frame,Riesz basis,Orthonormal basis,Atomic system
https://scma.maragheh.ac.ir/article_47114.html
https://scma.maragheh.ac.ir/article_47114_8902cf1717995f11537b68de849abfb0.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
On New Extensions of HermiteHadamard Inequalities for Generalized Fractional Integrals
73
88
EN
Huseyin
Budak
000000018843955X
Department of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey
hsyn.budak@gmail.com
Ebru
Pehlivan
Department of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey
ebrpehlivan.1453@gmail.com
Pınar
Kosem
Department of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey
pinarksm18@gmail.com
10.22130/scma.2020.121963.759
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 $k$RiemannLiouville fractional integrals as special cases of our main results. We also obtain some HermiteHadamard type inequalities by using the condition $f^{prime }(a+bx)geq f^{prime }(x)$ for all $xin left[ a,frac{a+b}{2}right] $ instead of convexity.
HermiteHadamard inequality,convex function,Bounded function
https://scma.maragheh.ac.ir/article_239415.html
https://scma.maragheh.ac.ir/article_239415_3352d66ff13ca0aaf786ddd8dec3bac3.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
Some biHamiltonian Systems and their Separation of Variables on 4dimensional Real Lie Groups
89
105
EN
Ghorbanali

Haghighatdoost
Department of Mathematics,Azarbaijan Shahid Madani University, 53714161, Tabriz, Iran.
gorbanali@yahoo.com
Salahaddin
AbdolhadiZangakani
Department of Mathematics, University of Bonab, Tabriz, Iran.
s.abdolhadi@ubonab.ac.ir
Rasoul
MahjoubiBahman
Department of Mathematics, University of Bonab, Tabriz, Iran.
r.mahjoubi@ubonab.ac.ir
10.22130/scma.2020.122380.764
In this work, we discuss biHamiltonian structures on a family of integrable systems on 4dimensional real Lie groups. By constructing the corresponding control matrix for this family of biHamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.
Integrable system,BiHamiltonian,Control matrix,Variables of separation
https://scma.maragheh.ac.ir/article_239419.html
https://scma.maragheh.ac.ir/article_239419_91691df474e29d99e062adb4b80f44ae.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
A Fixed Point Theorem for Weakly Contractive Mappings
107
122
EN
Morteza
Saheli
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
saheli@vru.ac.ir
Seyed Ali Mohammad
Mohsenialhosseini
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
amah@vru.ac.ir
10.22130/scma.2020.124853.778
In this paper, we generalize the concepts of weakly Kannan, weakly Chatterjea and weakly Zamfirescu for fuzzy metric spaces. Also, we investigate Banach's fixed point theorem for the mentioned classes of functions in these spaces. Moreover, we show that the class of weakly Kannan and weakly Chatterjea maps are subclasses of the class of weakly Zamfirescu maps.
Fixed point,Weakly Zamfirescu mappings,Weakly Kannan mappings,Weakly Chatterjea mappings,Weakly contractive mappings
https://scma.maragheh.ac.ir/article_240244.html
https://scma.maragheh.ac.ir/article_240244_312e08cfb7d0abd2e919ed27c0d60e88.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
23225807
24233900
18
1
2021
02
01
On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces
123
136
EN
N.
Seshagiri Rao
Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Post Box No.1888, Adama, Ethiopia.
seshu.namana@gmail.com
K.
Kalyani
0000000324096513
Department of Mathematics, Vignan's Foundation for Science, Technology & Research, Vadlamudi522213, Andhra Pradesh, India.
kalyani.namana@gmail.com
10.22130/scma.2020.120323.739
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.
Ordered metric space,Monotone property,Rational type contraction,Coupled fixed point
https://scma.maragheh.ac.ir/article_240245.html
https://scma.maragheh.ac.ir/article_240245_ff50f03d2067d187f5a7ed94298209a7.pdf