University of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators1153666010.22130/scma.2019.100821.542ENMohsenTaherniaDepartment of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.SirousMoradiDepartment of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Iran.SomayeJafariDepartment of Mathematics, Faculty of Science, Arak University, 38156-8-8349, Arak, Iran.Journal Article20190101In 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.https://scma.maragheh.ac.ir/article_36660_2dd27eb6ca24133e2c7b42b563bb1c1b.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Diameter Approximate Best Proximity Pair in Fuzzy Normed Spaces17343665910.22130/scma.2018.83850.420ENSeyed Ali MohammadMohsenialhosseiniFaculty of Mathematics, Yazd University, Yazd, Iran and Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.MortezaSaheliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20180407The 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.https://scma.maragheh.ac.ir/article_36659_89544cc8cecc2b2c61d92c42dffa6116.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Fixed Point Theory in $\varepsilon$-connected Orthogonal Metric Space35463636610.22130/scma.2018.72368.289ENMadjidEshaghi GordjiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.HastiHabibiDepartment of Mathematics, Semnan University, Semnan, Iran.Journal Article20170923The 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.https://scma.maragheh.ac.ir/article_36366_988f1f54affa1680ce562c8d50a002e5.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001$p$-adic Dual Shearlet Frames47563496510.22130/scma.2018.77684.355ENMahdiehFatemidokhtDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.AtaollahAskari HemmatDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.Journal Article20171221We 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 $L^2\left(Q_p^{2}\right)$. The discrete $p$-adic shearlet frames for $L^2\left(Q_p^{2}\right)$ is discussed. Also we prove that the frame operator $S$ associated with the group $G_p$ of all with the shearlet frame $SH\left( \psi; \Lambda\right)$ 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 $L^2\left(H\right)^{\vee}$ of $L^2\left(Q_p^{2}\right)$. Finally we give a necessary condition for two functions in $L^2\left(Q_p^{2}\right)$ to generate a p-adic dual shearlet tight frame via admissibility.https://scma.maragheh.ac.ir/article_34965_b1db50eb43891d7297fa1e8dc1a5b630.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Simple Construction of a Frame which is $\epsilon$-nearly Parseval and $\epsilon$-nearly Unit Norm57673605610.22130/scma.2018.79613.374ENMohammad AliHasankhani FardDepartment of Mathematics Vali-e-Asr University, Rafsanjan, Iran.Journal Article20180117In 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 $\left\{f_k\right\}_{k=1}^\infty$ and $\left\{Tf_k\right\}_{k=1}^\infty$ are $\epsilon$-nearly equal frame operators, where $\left\{f_k\right\}_{k=1}^\infty$ is a frame for $\mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.https://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain69813605710.22130/scma.2018.87581.449ENMuhamamdTahirDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.NazarKhanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.https://orcid.org/00Qazi ZahoorAhmadDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.BilalKhanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Gul MehtabKhanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Journal Article20180605The 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.https://scma.maragheh.ac.ir/article_36057_c5109d49de17a43b53100e7a3a2631d1.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework83913605810.22130/scma.2018.81285.391ENAliHuseynliDepartment 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.AsmarMirzabalayevaDepartment of Non-harmonic analysis", Institute of Mathematics and Mechanics of NAS of Azerbaijan, AZ1141, Baku, Azerbaijan.Journal Article20180213In 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\{A\left(t\right)e^{{\mathop{\rm int}} }; B\left(t\right)e^{-{\mathop{\rm int}} } \right\}_{n\in 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}^{+} $.https://scma.maragheh.ac.ir/article_36058_e30acb2ad0eafa93148679627a197562.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Generalized $F$-contractions in Partially Ordered Metric Spaces931043605910.22130/scma.2018.81871.398ENSeyede SamiraRazaviFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.HashemParvaneh MasihaFaculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.Journal Article20180220We 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.https://scma.maragheh.ac.ir/article_36059_bd5685c96b785d3676909c2ba3cf34a2.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Some Properties of $ \ast $-frames in Hilbert Modules Over Pro-C*-algebras1051173627810.22130/scma.2018.75253.328ENMonaNaroei IraniDepartment of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.AkbarNazariDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.0000000000000000Journal Article20171111In 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.https://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Some Results about the Contractions and the Pendant Pairs of a Submodular System1191283627910.22130/scma.2018.91924.481ENSaeidHanifehnezhadDepartment of Mathematics, Shahed University, Tehran, Iran.ArdeshirDolatiDepartment of Computer Science, Shahed University, Tehran, Iran.Journal Article20180814Submodularity 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 $\left(V,f\right)$ we construct a suitable sequence of $\left|V\right|-1$ 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.https://scma.maragheh.ac.ir/article_36279_8d135d8fd6e9c532ae60aff53488a3d6.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized $\Psi$-simulation Functions1291483636810.22130/scma.2018.78315.359ENGholamrezaHeidary JoonaghanyDepartment of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.AliFarajzadehDepartment of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran.0000-0001-5221-6741MahdiAzhiniDepartment of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.FarshidKhojastehDepartment of Mathematics, Faculty of Science, Arak Branch, Islamic Azad University, Arak, Iran.Journal Article20171229In 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.https://scma.maragheh.ac.ir/article_36368_2759917fb5f016efd9411aa212341008.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Coefficient Bounds for Analytic bi-Bazilevi\v{c} Functions Related to Shell-like Curves Connected with Fibonacci Numbers1491603605410.22130/scma.2018.82266.401ENHatun OzlemGuneyDicle University, Department of Mathematics, Science Faculty, TR-21280 Diyarbakir, Turkey.0000-0002-3010-7795Journal Article20180227In 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.https://scma.maragheh.ac.ir/article_36054_c859e3f5aa44c8ed0ef018ea37bd44a7.pdf