2021-10-19T18:07:52Z
https://scma.maragheh.ac.ir/?_action=export&rf=summon&issue=33108
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
Some Properties of Lebesgue Fuzzy Metric Spaces
Sugata
Adhya
Atasi
Deb Ray
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 well-known fuzzy metric spaces.
Fuzzy metric space
Lebesgue property
Weak $G$-complete
2021
02
01
1
14
https://scma.maragheh.ac.ir/article_46667_f59e7b832de5c1c96be81715fb591613.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
A Note on Some Results for $C$-controlled $K$-Fusion Frames in Hilbert Spaces
Habib
Shakoory
Reza
Ahmadi
Naghi
Behzadi
Susan
Nami
In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion 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
2021
02
01
15
34
https://scma.maragheh.ac.ir/article_46575_1c975979396a5c2cf12c24741735cc21.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
On Approximation of Some Mixed Functional Equations
Abbas
Najati
Batool
Noori
Mohammad Bagher
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 equations\begin{align*} 2\varphi(x + y) + \varphi(x - y) &= 3\varphi(x)+ 3\varphi(y) \\ 2\psi(x + y) + \psi(x - y) &= 3\psi(x) + 2\psi(y) + \psi(-y).\end{align*}We also consider the Pexider type functional equation \[2\psi(x + y) + \psi(x - y) = f(x) + g(y),\] and the additive functional equation\[2\psi(x + y) + \psi(x - y) = 3\psi(x) + \psi(y).\]
Hyers-Ulam stability
Additive
Quadratic
Drygas
Functional equation
Lebesgue measure zero
Pexider equation
2021
02
01
35
46
https://scma.maragheh.ac.ir/article_46665_3ce38b61e7b850642214401464923acf.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
Gabor Dual Frames with Characteristic Function Window
Mohammad Ali
Hasankhani Fard
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 $\left(\chi_{\left[c_1,d_1\right)},a,b\right)$ and $\left(\chi_{\left[c_2,d_2\right)},a,b\right)$ to form dual frames for $L_2\left(\mathbb{R}\right)$, 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
2021
02
01
47
57
https://scma.maragheh.ac.ir/article_46666_d613662078ce4df44a79d834be6b2f64.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
$K$-orthonormal and $K$-Riesz Bases
Ahmad
Ahmdi
Asghar
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.
$K$-frame
Riesz basis
Orthonormal basis
Atomic system
2021
02
01
59
72
https://scma.maragheh.ac.ir/article_47114_8902cf1717995f11537b68de849abfb0.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals
Huseyin
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 $x\in \left[ a,\frac{a+b}{2}\right] $ instead of convexity.
Hermite-Hadamard inequality
convex function
Bounded function
2021
02
01
73
88
https://scma.maragheh.ac.ir/article_239415_3352d66ff13ca0aaf786ddd8dec3bac3.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups
Ghorbanali
Haghighatdoost
Salahaddin
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.
Integrable system
Bi-Hamiltonian
Control matrix
Variables of separation
2021
02
01
89
105
https://scma.maragheh.ac.ir/article_239419_91691df474e29d99e062adb4b80f44ae.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
A Fixed Point Theorem for Weakly Contractive Mappings
Morteza
Saheli
Seyed Ali Mohammad
Mohsenialhosseini
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
2021
02
01
107
122
https://scma.maragheh.ac.ir/article_240244_312e08cfb7d0abd2e919ed27c0d60e88.pdf
Sahand Communications in Mathematical Analysis
SCMA
2322-5807
2322-5807
2021
18
1
On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces
N.
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.
Ordered metric space
Monotone property
Rational type contraction
Coupled fixed point
2021
02
01
123
136
https://scma.maragheh.ac.ir/article_240245_ff50f03d2067d187f5a7ed94298209a7.pdf