eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
1
15
10.22130/scma.2018.89571.471
34322
مقاله پژوهشی
The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
Kamal Fallahi
fallahi1361@gmail.com
1
Dragan Savic
gagasavic98@gmail.com
2
Ghasem Soleimani Rad
gh.soleimani2008@gmail.com
3
Department of Mathematics, Payame Noor University, Tehran, Iran.
Primary School ''Kneginja Milica", Beograd, Serbia.
Department of Mathematics, Payame Noor University, Tehran, Iran.
In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be generalized, improved, enriched and unified a number of recently announced results in the existing literature. Additionally, we elicit all of our main results by a non-trivial example and pose an interesting two open problems for the enthusiastic readers.
http://scma.maragheh.ac.ir/article_34322_c1a6f4a5bb424cbcce7290bf293886ca.pdf
$b$-metric space
$wt$-distance
Fixed point
Orbitally $G$-continuous mapping
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
17
30
10.22130/scma.2018.59792.211
31846
مقاله پژوهشی
$C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions
Arslan Hojat Ansari
analsisamirmath2@gmail.com
1
Tatjana Dosenovic
tatjanad@tf.uns.ac.rs
2
Stojan Radenovic
radens@beotel.net
3
Jeong Sheok Ume
jsume@changwon.ac.kr
4
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Faculty of Technology, Bulevar cara Lazara 1, University of Novi Sad, Serbia.
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.
Department of Mathematics, Changwon National University, Changwon, 641-773, Korea.
In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of functions which contains almost all known type contraction starting from 1922. year, respectively from famous Banach contraction principle. Three common fixed point theorems for four mappings are presented. The obtained results generalizes several existing ones<br />in literature.We finally propose three open problems.
http://scma.maragheh.ac.ir/article_31846_d6c970ed6b5f3e0d466239bb147f4213.pdf
Common fixed point
$varphi $-weakly contractive conditions
Complete metric space
Weakly compatible mappings
$C$-class function
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
31
50
10.22130/scma.2018.30018
30018
مقاله پژوهشی
Common Fixed Point Theory in Modified Intuitionistic Probabilistic Metric Spaces with Common Property (E.A.)
Hamid Shayanpour
h.shayanpour@sci.sku.ac.ir
1
Asiyeh Nematizadeh
a.nematizadeh@yahoo.com
2
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 88186-34141, Shahrekord, Iran.
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 88186-34141, Shahrekord, Iran.
In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and the common property (E.A.) in modified intuitionistic probabilistic metric spaces.<br />Then, by the common<br />property (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.
http://scma.maragheh.ac.ir/article_30018_01319582d03c748575cc8fcb9b401e9c.pdf
Modified intuitionistic probabilistic Menger metric space
Property (E.A.)
Common property (E.A.)
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
51
65
10.22130/scma.2018.73451.302
34300
مقاله پژوهشی
The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points
Seyfollah Mosazadeh
s.mosazadeh@kashanu.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran.
In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.
http://scma.maragheh.ac.ir/article_34300_558e5017059030a2a631d70b10382c96.pdf
Sturm-Liouville equation
Singular points
Turning points
Dual equations
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
67
81
10.22130/scma.2018.57727.199
32569
مقاله پژوهشی
Generalized Regular Fuzzy Irresolute Mappings and Their Applications
Elangovan Elavarasan
maths.aras@gmail.com
1
Department of Mathematics, Thiruvalluvar Arts and Science College (Affiliated to Thiruvalluvar University), Kurinjipadi, Tamil Nadu-607302, India.
In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open and generalized regular fuzzy irresolute closed maps in fuzzy topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy irresolute maps are investigated. As a natural follow-up of the study of r-generalized regular fuzzy open sets, the concept of r-generalized regular fuzzy connectedness of a fuzzy set is introduced and studied.
http://scma.maragheh.ac.ir/article_32569_defba3886a0dcdce9088bd3affc8b0d8.pdf
Generalized regular fuzzy irresolute
Generalized regular fuzzy irresolute open
Generalized regular fuzzy irresolute closed mapping
$r$-FRCO-$T_{1}$
$r$-FRCO-$T_{2}$
$r$-GRF-$T_{1}$
$r$-GRF-$T_{2}$
$r$-FRCO-regular
$r$-FRCO-normal
Strongly GRF-regular
strongly GRF-normal
$r$-GRF-separated sets
$r$-GRF-connectedness
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
83
92
10.22130/scma.2017.25887
25887
مقاله پژوهشی
Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces
Ebrahim Soori
sori.e@lu.ac.ir
1
Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran.
Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let $u, v$ be positive numbers. In this paper, we show that the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for finding a unique solution of the variational inequality for $(u, v)$-cocoercive mappings in Banach spaces.
http://scma.maragheh.ac.ir/article_25887_4d361d95ff4721a03622269726d897e2.pdf
Variational inequality
Nonexpansive mapping
$(u
v)$-cocoercive mapping
Metric projection
Sunny nonexpansive retraction
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
93
100
10.22130/scma.2017.28459
28459
مقاله پژوهشی
A class of new results in FLM algebras
Ali Naziri-Kordkandi
ali_naziri@pnu.ac.ir
1
Ali Zohri
zohri_a@pnu.ac.ir
2
Fariba Ershad
fershad@pnu.ac.ir
3
Bahman Yousefi
b_yousefi@pnu.ac.ir
4
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.
In this paper, we first derive some results by using the Gelfand spectrum and spectrum in FLM algebras. Then, the characterizations of multiplicative linear mappings are also discussed in these algebras.
http://scma.maragheh.ac.ir/article_28459_b7a5cf314e4ef6915c21f824caf64ba6.pdf
Fundamental topological algebra
FLM algebra
Spectrum
Multiplicative linear functional
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
101
114
10.22130/scma.2018.29983
29983
مقاله پژوهشی
Observational Modeling of the Kolmogorov-Sinai Entropy
Uosef Mohammadi
u.mohamadi@ujiroft.ac.ir
1
Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.
In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then the ergodic properties of relative semi-dynamical systems are investigated. Also, a relative version of Kolmogorov-Sinai theorem is given. Finally, it is proved that the relative entropy of a relative $ Theta $-measure preserving transformations with respect to a relative sub-$sigma_Theta$-algebra having finite atoms is affine.
http://scma.maragheh.ac.ir/article_29983_7a5face43ae162c0c5d62beecf8dc888.pdf
Relative entropy
Relative semi-dynamical system
$m_Theta$-equivalence
$m_Theta$-generator
$ (Theta_1
Theta_2) $-isomorphism
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
115
127
10.22130/scma.2018.62087.231
34323
مقاله پژوهشی
A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence
Moosa Ebadi
moosa.ebadi@yahoo.com
1
Farnaz Soltanpour
soltanpoor.farnaz@yahoo.com
2
Department of Mathematics, University of Farhangian, Tehran, Iran.
Department of Mathematics, University of Farhangian, Tehran, Iran.
In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore, new sequences have been used in order to introduce a new class of series. All properties of the sequences and related series are illustrated in the work by providing the details including sequences formula, related theorems, proofs and convergence analysis of the series.
http://scma.maragheh.ac.ir/article_34323_062ea721f5f1adbe65dd5025387cba8d.pdf
Fibonacci numbers
Golden Ratio
Convergence analysis
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
129
139
10.22130/scma.2018.68917.266
31814
مقاله پژوهشی
Richardson and Chebyshev Iterative Methods by Using G-frames
Hassan Jamali
jamali@vru.ac.ir
1
Mohsen Kolahdouz
mkolahdouz@post.vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern, Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.<br />In this paper, these schemes exploit the almost recently developed notion of g-frames which result in modified convergence rates compared with early computed ones in corresponding classical formulations. <br />In fact, these convergence rates are formed by the lower and upper bounds of the given g-frame. Therefore, we can determine any convergence rate by considering an appropriate g-frame.
http://scma.maragheh.ac.ir/article_31814_ef793a9c97fed9f9c9716480c9dad7d0.pdf
Hilbert space
$g$-frame
Operator equation
Iterative method
Chebyshev polynomials
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
141
152
10.22130/scma.2017.29018
29018
مقاله پژوهشی
Some Fixed Point Results on Intuitionistic Fuzzy Metric Spaces with a Graph
Mohammad Esmael Samei
me_samei@yahoo.com
1
Department of Mathematics, Faculty of Science, University of Bu-Ali Sina, P.O.Box 6517838695, Hamedan, Iiran.
In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory<br />and graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, we present some iterative scheme results for $G$-fuzzy contractive and $G$-fuzzy nonexpansive mappings on graphs.
http://scma.maragheh.ac.ir/article_29018_3207b7fee935ce78fea9497d8eb53f58.pdf
Fixed point
Intuitionistice fuzzy metric space
Connected graph
$G$-fuzzy contractive
$G$-fuzzy nonexpansive
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
153
163
10.22130/scma.2018.62262.233
30861
مقاله پژوهشی
On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras
Seyed Mohammad Sadegh Nabavi Sales
sadegh.nabavi@gmail.com
1
Department of Mathematics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.
http://scma.maragheh.ac.ir/article_30861_f0543a2f5639a20e512cc2c244fb4bd2.pdf
Approximate orthogonality
Birkhoff--James orthogonality
Range-kernel orthogonality
$C^ast$-algebra
$ast$-orthogonality
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
165
177
10.22130/scma.2018.59232.206
34304
مقاله پژوهشی
Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames
Azadeh Alijani
a.alijani57@gmail.com
1
Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.
Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. We obtain a $*$-frame by an orthogonal projection and a given $*$-frame, characterize its duals, and give a bilateral condition for commutating frame operator of a primary $*$-frame and an orthogonal projection. At the end of paper, pre-frame operator of a dual frame is computed by pre-frame operator of a general $*$-frame and an orthogonal projection.
http://scma.maragheh.ac.ir/article_34304_f1fa1d7d30cfa5a319737d9fba040b79.pdf
Dual frame
Equivalent $*$-frame
Frame operator
$*$-frame
Operator dual frame
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
179
212
10.22130/scma.2017.29263
29263
مقاله پژوهشی
Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces
Roghaye Jalal Shahkoohi
rog.jalal@gmail.com
1
Zohreh Bagheri
zohrehbagheri@yahoo.com
2
Department of Mathematics, Aliabad katoul Branch, Islamic Azad University, Aliabad katoul, Iran.
Department of Mathematics, Azadshahr Branch, Islamic Azad University, Azadshahr, Iran.
In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces. These include Geraghty-type conditions, conditions that use comparison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, textit{e.g.}, in [21] and [22]. In the last section of the paper, we define the notion of almost generalized $(psi ,varphi )_{s,a}$-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of Ciric et.al. in [23] to the setting of $b_{2}$-metric spaces. Also, some examples are provided to illustrate the results presented herein and several interesting consequences of our theorems are also provided. The findings of the paper are based on generalization and modification of some recently reported theorems in the literature.
http://scma.maragheh.ac.ir/article_29263_f6da7913f6ba4c54cf195c5e7a308a31.pdf
Fixed point
Complete metric space
Ordered $b_2$-metric space
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2019-02-01
13
1
213
240
10.22130/scma.2018.30145
30145
مقاله پژوهشی
Surjective Real-Linear Uniform Isometries Between Complex Function Algebras
Hadis Pazandeh
pazandeh63@gmail.com
1
Davood Alimohammadi
alimohammadi.davood@gmail.com
2
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.
In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$, where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T $ whenever $ A $ and $ B $ are complex function algebras and $ T $ does not assume to be unit-preserving.
http://scma.maragheh.ac.ir/article_30145_1313cd222b3fef5233599be64c52c1b4.pdf
Choquet boundary
Function algebra
Function space
Real-linear uniform isometry