University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators
1
15
EN
Mohsen
Tahernia
Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.
m.taherniamath@gmail.com
Sirous
Moradi
Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.
sirousmoradi@gmail.com
Somaye
Jafari
Department of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.
s.jafari.math@gmail.com
10.22130/scma.2019.100821.542
In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of common zeros of operators.
Maximal monotone operator,Proximal point algorithm,Nonexpansive map,Resolvent operator
https://scma.maragheh.ac.ir/article_36660.html
https://scma.maragheh.ac.ir/article_36660_2dd27eb6ca24133e2c7b42b563bb1c1b.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces
17
34
EN
Seyed Ali Mohammad
Mohsenialhosseini
Faculty of Mathematics, Yazd University, Yazd, Iran and Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
mohsenhosseini@yazd.ac.ir
Morteza
Saheli
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
saheli@vru.ac.ir
10.22130/scma.2018.83850.420
The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. Using these results, we prove theorems for various types of well-known generalized contractions in fuzzy normed spaces. Also, we apply our results to get an application of approximate fixed point and approximate best proximity pair theorem of their diameter.
Cyclic maps,$alpha$-asymptotically regular,$F$-Kannan operator,Fuzzy diameter
https://scma.maragheh.ac.ir/article_36659.html
https://scma.maragheh.ac.ir/article_36659_89544cc8cecc2b2c61d92c42dffa6116.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Fixed Point Theory in $varepsilon$-connected Orthogonal Metric Space
35
46
EN
Madjid
Eshaghi Gordji
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.
meshaghi@semnan.ac.ir
Hasti
Habibi
Department of Mathematics, Semnan University, Semnan, Iran.
hastihabibi1363@gmail.com
10.22130/scma.2018.72368.289
The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some illustrating examples.
Fixed point,$varepsilon$-connected,Orthogonal set,solution,Metric space,Analytic function
https://scma.maragheh.ac.ir/article_36366.html
https://scma.maragheh.ac.ir/article_36366_988f1f54affa1680ce562c8d50a002e5.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
$p$-adic Dual Shearlet Frames
47
56
EN
Mahdieh
Fatemidokht
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
fatemidokht@gmail.com
Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
askari@uk.ac.ir
10.22130/scma.2018.77684.355
We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for $L^2left(Q_p^{2}right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SHleft( psi; Lambdaright)$ is a Fourier multiplier with a function in terms of $widehat{psi}$. For a measurable subset $H subset Q_p^{2}$, we considered a subspace $L^2left(Hright)^{vee}$ of $L^2left(Q_p^{2}right)$. Finally we give a necessary condition for two functions in $L^2left(Q_p^{2}right)$ to generate a p-adic dual shearlet tight frame via admissibility.
$p$-adic numbers,Dual frame,$p$-adic shearlet system,$p$-adic dual tight frame
https://scma.maragheh.ac.ir/article_34965.html
https://scma.maragheh.ac.ir/article_34965_b1db50eb43891d7297fa1e8dc1a5b630.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm
57
67
EN
Mohammad Ali
Hasankhani Fard
Department of Mathematics Vali-e-Asr University, Rafsanjan, Iran.
m.hasankhani@vru.ac.ir
10.22130/scma.2018.79613.374
In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible operators $T$ on the finite or infinite dimensional Hilbert space $mathcal{H}$ such that $left{f_kright}_{k=1}^infty$ and $left{Tf_kright}_{k=1}^infty$ are $epsilon$-nearly equal frame operators, where $left{f_kright}_{k=1}^infty$ is a frame for $mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.
Frame,Parseval frame,$epsilon$-nearly Parseval frame,$epsilon$-nearly equal frame operators,Operator dual Parseval frames
https://scma.maragheh.ac.ir/article_36056.html
https://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain
69
81
EN
Muhamamd
Tahir
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
tahirmuhammad778@gmail.com
Nazar
Khan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
nazarmaths@gmail.com
Qazi Zahoor
Ahmad
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
zahoorqazi5@gmail.com
Bilal
Khan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
bilalmaths789@gmail.com
Gul Mehtab
Khan
Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.
mehtabmaths789@gmail.com
10.22130/scma.2018.87581.449
The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier known developments.
Univalent function,Analytic function,Bi-univalent function,Subordination between analytic functions,Starlike and strongly starlike functions,Conic domain
https://scma.maragheh.ac.ir/article_36057.html
https://scma.maragheh.ac.ir/article_36057_c5109d49de17a43b53100e7a3a2631d1.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework
83
91
EN
Ali
Huseynli
Department of Mathematics, Khazar University, AZ1096, Baku, Azerbaijan and Department of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.
alihuseynli@gmail.com
Asmar
Mirzabalayeva
Department of Non-harmonic analysis", Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.
esmer26@mail.ru
10.22130/scma.2018.81285.391
In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is bounded in $L_{p;r} $. The problem of basisness of the system $left{Aleft(tright)e^{{mathop{rm int}} }; Bleft(tright)e^{-{mathop{rm int}} } right}_{nin Z_{+} }, $ is also considered. It is shown that under an additional condition this system forms a basis in $L_{p;r} $ if and only if the Riemann-Hilbert problem has a unique solution in corresponding Hardy class ${ H}_{p;r}^{+} times { H}_{p;r}^{+} $.
Function space,Hardy class,singular integral,Riemann-Hilbert problem
https://scma.maragheh.ac.ir/article_36058.html
https://scma.maragheh.ac.ir/article_36058_e30acb2ad0eafa93148679627a197562.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Generalized $F$-contractions in Partially Ordered Metric Spaces
93
104
EN
Seyede Samira
Razavi
Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
srazavi@mail.kntu.ac.ir
Hashem
Parvaneh Masiha
Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.
masiha@kntu.ac.ir
10.22130/scma.2018.81871.398
We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contraction mapping. We also prove some fixed point results about this notion in partially ordered metric spaces. We also provide an example to support our results. In fact, this example shows that our main theorem is a genuine generalization in the area of the generalized $F$-contraction mappings in partially ordered metric spaces.
Fixed point,$F$-contraction,Ordered weakly $F$-contraction,Generalized $F$-contraction,$acute{mathrm{C}}$iri$acute{mathrm{c}}$ type mappings
https://scma.maragheh.ac.ir/article_36059.html
https://scma.maragheh.ac.ir/article_36059_bd5685c96b785d3676909c2ba3cf34a2.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras
105
117
EN
Mona
Naroei Irani
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
m.naroei.math@gmail.com
Akbar
Nazari
0000000000000000
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
nazari@uk.ac.ir
10.22130/scma.2018.75253.328
In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modules over pro-C*-algebras and investigate conditions that under which the sequence ${ { {h_i} }_{i in I} }$ is a standard $ ast $-frame of multipliers for Hilbert modules over pro-C*-algebras. Also the effect of operators on standard $ ast $-frames of multipliers for $ E $ is examined. Finally, compositions of standard $ ast $-frames in Hilbert modules over pro-C*-algebras are studied.
Hilbert modules over pro-C*-algebras,Standard $ ast $-frame of multipliers,$ ast $-frame operator,Pre-$ ast $-frame
https://scma.maragheh.ac.ir/article_36278.html
https://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Some Results about the Contractions and the Pendant Pairs of a Submodular System
119
128
EN
Saeid
Hanifehnezhad
Department of Mathematics, Shahed University, Tehran, Iran.
saeid.hanifehnezhad@gmail.com
Ardeshir
Dolati
Department of Computer Science, Shahed University, Tehran, Iran.
dolati@shahed.ac.ir
10.22130/scma.2018.91924.481
Submodularity is an important property of set functions with deep theoretical results and various applications. Submodular systems appear in many applicable area, for example machine learning, economics, computer vision, social science, game theory and combinatorial optimization. Nowadays submodular functions optimization has been attracted by many researchers. Pendant pairs of a symmetric submodular system play essential role in finding a minimizer of this system. In this paper, we investigate some relations between pendant pairs of a submodular system and pendant pairs of its contractions. For a symmetric submodular system $left(V,fright)$ we construct a suitable sequence of $left|Vright|-1$ pendant pairs of its contractions. By using this sequence, we present some properties of the system and its contractions. Finally, we prove some results about the minimizers of a posimodular function.
Submodular system,Submodular optimization,Maximum adjacency ordering,Posimodular functions,Pendant pairs,st-cut
https://scma.maragheh.ac.ir/article_36279.html
https://scma.maragheh.ac.ir/article_36279_8d135d8fd6e9c532ae60aff53488a3d6.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized $Psi$-simulation Functions
129
148
EN
Gholamreza
Heidary Joonaghany
Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Ali
Farajzadeh
0000-0001-5221-6741
Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.
farajzadehali@gmail.com
Mahdi
Azhini
Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
mahdi.azhini@gmail.com
Farshid
Khojasteh
Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad University, Arak, Iran.
f-khojaste@iau-arak.ac.ir
10.22130/scma.2018.78315.359
In this paper, a new stratification of mappings, which is called $Psi$-simulation functions, is introduced to enhance the study of the Suzuki type weak-contractions. Some well-known results in weak-contractions fixed point theory are generalized by our researches. The methods have been appeared in proving the main results are new and different from the usual methods. Some suitable examples are furnished to demonstrate the validity of the hypothesis of our results and reality of our generalizations.
Common fixed point,Suzuki type contractions,Generalized $Psi$-simulation functions
https://scma.maragheh.ac.ir/article_36368.html
https://scma.maragheh.ac.ir/article_36368_2759917fb5f016efd9411aa212341008.pdf
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
16
1
2019
10
01
Coefficient Bounds for Analytic bi-Bazileviv{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers
149
160
EN
Hatun Ozlem
Guney
0000-0002-3010-7795
Dicle University, Department of Mathematics, Science Faculty, TR-21280 Diyarbakir, Turkey.
ozlemg@dicle.edu.tr
10.22130/scma.2018.82266.401
In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers. Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.
Bi-Bazilevic function,Analytic function,Shell-like curve,Fibonacci numbers
https://scma.maragheh.ac.ir/article_36054.html
https://scma.maragheh.ac.ir/article_36054_c859e3f5aa44c8ed0ef018ea37bd44a7.pdf