University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application1153432210.22130/scma.2018.89571.471ENKamal FallahiDepartment of Mathematics, Payame Noor University, Tehran, Iran.0000-0003-3400-4424Dragan SavicPrimary School ''Kneginja Milica", Beograd, Serbia.Ghasem Soleimani RadDepartment of Mathematics, Payame Noor University, Tehran, Iran.0000-0002-0758-2758Journal Article20180717In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201$C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions17303184610.22130/scma.2018.59792.211ENArslan Hojat AnsariDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.Tatjana DosenovicFaculty of Technology, Bulevar cara Lazara 1, University of Novi Sad, Serbia.Stojan RadenovicFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.Jeong Sheok UmeDepartment of Mathematics, Changwon National University, Changwon, 641-773, Korea.Journal Article20170224In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Common Fixed Point Theory in Modified Intuitionistic Probabilistic Metric Spaces with Common Property (E.A.)31503001810.22130/scma.2018.30018ENHamid ShayanpourDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 88186-34141, Shahrekord, Iran.Asiyeh NematizadehDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O.Box 88186-34141, Shahrekord, Iran.Journal Article20170203In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points51653430010.22130/scma.2018.73451.302ENSeyfollah MosazadehDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran.Journal Article20171011In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Generalized Regular Fuzzy Irresolute Mappings and Their Applications67813256910.22130/scma.2018.57727.199ENElangovan ElavarasanDepartment of Mathematics, Thiruvalluvar Arts and Science College (Affiliated to Thiruvalluvar University), Kurinjipadi, Tamil Nadu-607302, India.Journal Article20170125In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Extensions of Saeidi's Propositions for Finding a Unique Solution of a Variational Inequality for $(u,v)$-cocoercive Mappings in Banach Spaces83922588710.22130/scma.2017.25887ENEbrahim SooriDepartment of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran.Journal Article20160626Let $C$ 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201A class of new results in FLM algebras931002845910.22130/scma.2017.28459ENAli Naziri-KordkandiDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.Ali ZohriDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.0000-0001-7829-5599Fariba ErshadDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.Bahman YousefiDepartment of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, I.R. of Iran.Journal Article20170214In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Observational Modeling of the Kolmogorov-Sinai Entropy1011142998310.22130/scma.2018.29983ENUosef MohammadiDepartment of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.Journal Article20170120In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence1151273432310.22130/scma.2018.62087.231ENMoosa EbadiDepartment of Mathematics, University of Farhangian, Tehran, Iran.Farnaz SoltanpourDepartment of Mathematics, University of Farhangian, Tehran, Iran.Journal Article20170417In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Richardson and Chebyshev Iterative Methods by Using G-frames1291393181410.22130/scma.2018.68917.266ENHassan JamaliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Mohsen KolahdouzDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20170727In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Some Fixed Point Results on Intuitionistic Fuzzy Metric Spaces with a Graph1411522901810.22130/scma.2017.29018ENMohammad Esmael SameiDepartment of Mathematics, Faculty of Science, University of Bu-Ali Sina, P.O.Box 6517838695, Hamedan, Iiran.0000-0002-5450-3127Journal Article20161202In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras1531633086110.22130/scma.2018.62262.233ENSeyed Mohammad Sadegh Nabavi SalesDepartment of Mathematics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.Journal Article20170418We 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Duals of Some Constructed $*$-Frames by Equivalent $*$-Frames1651773430410.22130/scma.2018.59232.206ENAzadeh AlijaniDepartment of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan, P.O. Box 7719758457, Rafsanjan, Iran.Journal Article20170215Hilbert 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered $b_2$-metric Spaces1792122926310.22130/scma.2017.29263ENRoghaye Jalal ShahkoohiDepartment of Mathematics, Aliabad katoul Branch, Islamic Azad University, Aliabad katoul, Iran.Zohreh BagheriDepartment of Mathematics, Azadshahr Branch, Islamic Azad University, Azadshahr, Iran.Journal Article20170123In 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.University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Surjective Real-Linear Uniform Isometries Between Complex Function Algebras2132403014510.22130/scma.2018.30145ENHadis PazandehDepartment of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.Davood AlimohammadiDepartment of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Arak, Iran.Journal Article20170619In 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.