فهرست مطالب

Sahand Communications in Mathematical Analysis - Volume:16 Issue:1, 2019
  • Volume:16 Issue:1, 2019
  • تاریخ انتشار: 1398/07/09
  • تعداد عناوین: 12
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  • Mohsen Tahernia, Sirous Moradi *, Somaye Jafari Pages 1-15
    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.
    Keywords: Maximal monotone operator, Proximal point algorithm, Nonexpansive map, Resolvent operator
  • Seyed Ali Mohammad Mohsenialhosseini, Morteza Saheli * Pages 17-34
    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.
    Keywords: Cyclic maps, $alpha$-asymptotically regular, $F$-Kannan operator, Fuzzy diameter
  • Madjid Eshaghi Gordji, Hasti Habibi * Pages 35-46
    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.
    Keywords: Fixed point, $varepsilon$-connected, Orthogonal set, solution, Metric space, Analytic function
  • Mahdieh Fatemidokht, Ataollah Askari Hemmat * Pages 47-56
    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.
    Keywords: $p$-adic numbers, Dual frame, $p$-adic shearlet system, $p$-adic dual tight frame
  • Mohammad Ali Hasankhani Fard * Pages 57-67

    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.

    Keywords: Frame, Parseval frame, $epsilon$-nearly Parseval frame, $epsilon$-nearly equal frame operators, Operator dual Parseval frames
  • Muhamamd Tahir, Nazar Khan, Qazi Zahoor Ahmad, Bilal Khan *, Gul Mehtab Khan Pages 69-81
    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.
    Keywords: Univalent function, Analytic function, Bi-univalent function, Subordination between analytic functions, Starlike, strongly starlike functions, Conic domain
  • Ali Huseynli *, Asmar Mirzabalayeva Pages 83-91

    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}^{+} $.

    Keywords: Function space, Hardy class, singular integral, Riemann-Hilbert problem
  • Seyede Samira Razavi, Hashem Parvaneh Masiha * Pages 93-104
    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.
    Keywords: Fixed point, $F$-contraction, Ordered weakly $F$-contraction, Generalized $F$-contraction, $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type mappings
  • Mona Naroei Irani, Akbar Nazari * Pages 105-117
    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.
    Keywords: Hilbert modules over pro-C*-algebras, Standard $ ast $-frame of multipliers, $ ast $-frame operator, Pre-$ ast $-frame
  • Saeid Hanifehnezhad, Ardeshir Dolati * Pages 119-128
    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.
    Keywords: Submodular system, Submodular optimization, Maximum adjacency ordering, Posimodular functions, Pendant pairs, st-cut
  • Gholamreza Heidary Joonaghany, Ali Farajzadeh *, Mahdi Azhini, Farshid Khojasteh Pages 129-148
    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.
    Keywords: Common fixed point, Suzuki type contractions, Generalized $Psi$-simulation functions
  • Hatun Ozlem Guney * Pages 149-160
    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.
    Keywords: Bi-Bazilevic function, Analytic function, Shell-like curve, Fibonacci numbers