University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
Caristi Type Cyclic Contraction and Coupled Fixed Point Results in Bipolar Metric Spaces
1
22
EN
Gagula Naveen Venkata
Kishore
Department of Mathematics, Sagi Rama Krishnam Raju Engineering College, Bhimavaram, West Godavari - 534 204, Andhra Pradesh, India.
kishore.apr2@gmail.com
Bagathi
Srinuvasa Rao
Department of Mathematics, Dr.B.R.Ambedkar University,
Srikakulam, Etcherla - 532410, Andhra Pradesh, India.
srinivasabagathi@gmail.com
Stojan
Radenovic
Department Faculty of Mechanical Engineering, University of Belgrade, Belgrade.
radens@beotel.net
Huaping
Huang
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China.
mathhhp@163.com
10.22130/scma.2018.79219.369
In this paper, we establish the existence of common coupled fixed point results for new Caristi type contraction of three covariant mappings in Bipolar metric spaces. Some interesting consequences of our results are achieved. Moreover, we give an illustration which presents the applicability of the achieved results.
Bipolar metric space,Compatible mappings,Coupled fixed point,Common fixed point
https://scma.maragheh.ac.ir/article_36736.html
https://scma.maragheh.ac.ir/article_36736_824af8900579b930f3348c42ac9de92d.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
A Version of Favard's Inequality for the Sugeno Integral
23
37
EN
Bayaz
Daraby
0000-0001-6872-8661
Department of Mathematics, University of Maragheh, Maragheh, Iran.
bdaraby@maragheh.ac.ir
Hassan
Ghazanfary Asll
Ph.D. student of Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
h_ghazanfary@sut.ac.ir
IldarI
Sadeqi
0000-0001-5336-6186
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
esadeqi@sut.ac.ir
10.22130/scma.2020.119368.728
In this paper, we present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.
Favard's inequality,Sugeno integral,Fuzzy measure,Fuzzy integral inequality
https://scma.maragheh.ac.ir/article_38119.html
https://scma.maragheh.ac.ir/article_38119_5654c1b9174f9fe4f8c78f32a15f6c48.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
Continuous $k$-Fusion Frames in Hilbert Spaces
39
55
EN
Vahid
Sadri
Department of Mathematics, Shabestar Branch, Islamic Azad University Shabestar, Iran.
vahidsadri57@gmail.com
Reza
Ahmadi
Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.
rahmadi@tabrizu.ac.ir
Mohammad
Jafarizadeh
Faculty of Physic, University of Tabriz,
Tabriz, Iran.
jafarizadeh@tabrizu.ac.ir
Susan
Nami
Faculty of Physic, University of Tabriz,
Tabriz, Iran.
s.nami@tabrizu.ac.ir
10.22130/scma.2018.83792.418
The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames which is important for frame applications, have been specified completely for the continuous frames. After improving and extending the concept of fusion frames and continuous frames, in this paper we introduce continuous $k$-fusion frames in Hilbert spaces. Similarly to the c-fusion frames, dual of continuous $k$-fusion frames may not be defined, we however define the $Q$-dual of continuous $k$-fusion frames. Also some new results and the perturbation of continuous $k$-fusion frames will be presented.
Fusion frame,$k$-fusion frame,c$k$-fusion frame,Q-duality
https://scma.maragheh.ac.ir/article_36737.html
https://scma.maragheh.ac.ir/article_36737_f74af2ceb97b56960df44e5c8826e4a5.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
On $F$-Weak Contraction of Generalized Multivalued Integral Type Mappings with $alpha $-admissible
57
67
EN
Vatan
Karakaya
Department of Mathematical Engineering, Yildiz Technical
University, Davutpasa Campus, Esenler, 34210 Istanbul, Turkey.
vkkaya@yahoo.com
Necip
Şimşek
Department of Mathematics, Istanbul Commerce University, Sutluce Campus, Beyoglu, 34445 Istanbul, Turkey.
necsimsek@yahoo.com
Derya
Sekman
Department of Mathematics, Ahi Evran University, Bagbasi
Campus, 40100 Kirsehir, Turkey.
deryasekman@gmail.com
10.22130/scma.2018.83065.407
The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the other important classes. Along with that, α-admissible mapping is a different approach in the fixed point theory. According to this method, a single or multivalued mapping does not have a fixed point in general. But, under some restriction on the mapping, a fixed point can be obtained. In this article, we combine four significant notions and also establish fixed point theorem for this mappings in complete metric spaces. Moreover, we give an example to show the interesting of our results according to earlier results in literature.
Fixed point theory,$alpha $-admissible mappings,Multivalued integral operators,$F$-weak contraction
https://scma.maragheh.ac.ir/article_36969.html
https://scma.maragheh.ac.ir/article_36969_422f3324a20e4977c2282de6a0fb9d68.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$beta$-Banach Spaces
69
90
EN
Prondanai
Kaskasem
0000-0003-4517-5106
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
prondanaik@nu.ac.th
Aekarach
Janchada
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
aiaek10@gmail.com
Chakkrid
Klin-eam
0000-0001-7943-8176
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand and Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, 65000, Thailand.
chakkridk@nu.ac.th
10.22130/scma.2018.87694.451
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation<br />[<br /> fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),<br />]<br /> where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generalized radical cubic functional equations in $(beta,p)$-Banach spaces.
Hyers-Ulam-Rassias stability,radical cubic functional equation,quasi-$beta$-normed spaces,subadditive function
https://scma.maragheh.ac.ir/article_37191.html
https://scma.maragheh.ac.ir/article_37191_23668c1e86441667a12fea82395eabf1.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
A Common Fixed Point Theorem Using an Iterative Method
91
98
EN
Ali
Bagheri Vakilabad
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
alibagheri1385@yahoo.com
10.22130/scma.2019.71435.281
Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set $C$ and finite many mappings from $C$ in to $H$, to obtain a converging sequence to a common fixed point for these non-self and non-expansive mappings.
Hilbert space,Nonexpansive mapping,Krasnoselskii-Mann iterative method,Inward condition
https://scma.maragheh.ac.ir/article_37370.html
https://scma.maragheh.ac.ir/article_37370_23b71732cb85f46fa137d11f68350735.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
About One Sweep Algorithm for Solving Linear-Quadratic Optimization Problem with Unseparated Two-Point Boundary Conditions
99
107
EN
Fikret
A. Aliev
Institute of Applied Mathematics, BSU, Baku, Azerbaijan.
f_aliev@yahoo.com
Mutallim
M. Mutallimov
0000-0001-8353-9295
Institute of Applied Mathematics, BSU, Baku, Azerbaijan.
mmutallimov@bsu.edu.az
Ilkin
A. Maharramov
Institute of Applied Mathematics, BSU, Baku, Azerbaijan.
ilkin_072@mail.ru
Nargiz
Sh. Huseynova
Institute of Applied Mathematics, BSU, Baku, Azerbaijan.
nargiz_huseynova@yahoo.com
Leyla
I. Amirova
Institute of Applied Mathematics, BSU, Baku, Azerbaijan.
kamhas06@rambler.ru
10.22130/scma.2019.107161.605
In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new sweep algorithm which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimization problems encounters serious difficulties in passing through nodal points. The results are illustrated with a specific numerical example.
Sweep Algorithm,Optimization,unseparated two-point boundary conditions,Riccati equations
https://scma.maragheh.ac.ir/article_37833.html
https://scma.maragheh.ac.ir/article_37833_54d6126205a68ce8ec09a67f2f92ea24.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
Estimates of Norm and Essential norm of Differences of Differentiation Composition Operators on Weighted Bloch Spaces
109
124
EN
Mostafa
Hassanloo
Engineering Faculty of Khoy, Urmia University, Urmia, Iran.
m.hassanlou@urmia.ac.ir
10.22130/scma.2019.101527.551
Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.
Differentiation composition operators,Weighted Bloch spaces,Essential norm
https://scma.maragheh.ac.ir/article_37200.html
https://scma.maragheh.ac.ir/article_37200_d3489951611926ddb21b589b0f75ec2e.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
On Preserving Properties of Linear Maps on $C^{*}$-algebras
125
137
EN
Fatemeh
Golfarshchi
Department of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.
f.golfarshchi@tabriziau.ac.ir
Ali Asghar
Khalilzadeh
Department of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.
khalilzadeh@sut.ac.ir
10.22130/scma.2019.107553.607
Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorphism. It is also shown that if $varphi(|ab|)=|varphi(a)varphi(b)|$ for all $a,bin A$, then $varphi$ is a unital $*$-homomorphism.
Absolute value preserving,$*$-homomorphism,Unitary preserving,numerical range
https://scma.maragheh.ac.ir/article_37336.html
https://scma.maragheh.ac.ir/article_37336_c7070f356e0ff49cbe395cf74a73eedd.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
An Example of Data Dependence Result for The Class of Almost Contraction Mappings
139
155
EN
Yunus
Atalan
Department of Mathematics, Faculty of Science and Arts, Aksaray University, Aksaray Turkey.
yunus_atalan@hotmail.com
Vatan
Karakaya
Department of Mathematical Engineering,Y\i ld\i z Technical University, Davutpasa Campus, Esenler, 34210 Istanbul, Turkey.
vkkaya@yahoo.com
10.22130/scma.2018.88562.464
In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. Finally, we obtain a data dependence result for almost contraction mappings by using $S^*$ iteration method and in order to show validity of this result we give an example.
Iteration Methods,Convergence analysis,Data dependence,Almost contraction mappings
https://scma.maragheh.ac.ir/article_37337.html
https://scma.maragheh.ac.ir/article_37337_a41ff9c0bfe26b1c38ca2dc551410b9c.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
17
1
2020
01
01
On Sum and Stability of Continuous $G$-Frames
157
169
EN
Azam
Yousefzadeheyni
Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.
azamyousefzadeh@gmail.com
Mohammad Reza
Abdollahpour
Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.
mrabdollahpour@yahoo.com
10.22130/scma.2018.90101.472
In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.
Continuous $g$-frame,Parseval continuous $g$-frame,Continuous $g$-Bessel family,stability
https://scma.maragheh.ac.ir/article_37340.html
https://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf