فهرست مطالب

Sahand Communications in Mathematical Analysis - Volume:13 Issue: 1, 2019
  • Volume:13 Issue: 1, 2019
  • تاریخ انتشار: 1397/12/20
  • تعداد عناوین: 15
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  • Kamal Fallahi *, Dragan Savic, Ghasem Soleimani Rad Pages 1-15
    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.
    Keywords: b-metric space, wt-distance, Fixed point, Orbitally G-continuous mapping
  • Arslan Hojat Ansari, Tatjana Dosenovic *, Stojan Radenovic, Jeong Sheok Ume Pages 17-30
    In this paper, we discuss and extend some recent common fixed point results established by using φ− 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 in literature.We finally propose three open problems.
    Keywords: Common fixed point, ?-weakly contractive conditions, Complete metric space, Weakly compatible mappings, C-class function
  • Hamid Shayanpour, Asiyeh Nematizadeh * Pages 31-50
    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. Then, by the common property (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.
    Keywords: Modified intuitionistic probabilistic Menger metric space, Property (E.A.), Common property (E.A.)
  • Seyfollah Mosazadeh * Pages 51-65
    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.
    Keywords: Sturm-Liouville equation, Singular points, Turning points, Dual equations
  • Elangovan Elavarasan * Pages 67-81
    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.
    Keywords: Generalized regular fuzzy irresolute, Generalized regular fuzzy irresolute open, Generalized regular fuzzy irresolute closed mapping, r -FRCO-T1, r-FRCO-T2, r-GRF-T1, r-GRF-T2, r-FRCO-regular, r-FRCO-normal, Strongly GRF-regular, strongly GRF-normal, r-GRF-separated sets, r-GRF-connectedness
  • Ebrahim Soori * Pages 83-92
    Let Cbe a nonempty closed convex subset of a real Banach space E, let B:C→E be a nonlinear map, and let u,v be positive numbers. In this paper, we show that the generalized variational inequality VI(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.
    Keywords: Variational inequality, Nonexpansive mapping, $(u, v)$-cocoercive mapping, Metric projection, Sunny nonexpansive retraction
  • Ali Naziri, Kordkandi *, Ali Zohri, Fariba Ershad, Bahman Yousefi Pages 93-100
    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.
    Keywords: Fundamental topological algebra, FLM algebra, Spectrum, Multiplicative linear functional
  • Uosef Mohammadi * Pages 101-114
    In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer Θ. The relative entropy of a sub-σΘ-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 Θ-measure preserving transformations with respect to a relative sub-σΘ -algebra having finite atoms is affine.
    Keywords: Relative entropy, Relative semi-dynamical system, m?-equivalence, m?-generator, $ (-Theta1 -Theta2) $-isomorphism
  • Moosa Ebadi *, Farnaz Soltanpour Pages 115-127
    In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. 1+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.
    Keywords: Fibonacci numbers, Golden Ratio, Convergence analysis
  • Hassan Jamali *, Mohsen Kolahdouz Pages 129-139
    In this paper, we design some iterative schemes for solving operator equation Lu=f , where L:H→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. 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. 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.
    Keywords: Hilbert space, g-frame, Operator equation, Iterative method, Chebyshev polynomials
  • Mohammad Esmael Samei * Pages 141-152
    In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory 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.
    Keywords: Fixed point, Intuitionistice fuzzy metric space, Connected graph, G-fuzzy contractive, G-fuzzy nonexpansive
  • Seyed Mohammad Sadegh Nabavi Sales * Pages 153-163
    We offer a new definition of ε -orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of ε-orthogonality in an arbitrary C∗-algebra A, as a Hilbert C∗-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in C∗ -algebras.
    Keywords: Approximate orthogonality, Birkhoff--James orthogonality, Range-kernel orthogonality, C?-algebra, ?-orthogonality
  • Azadeh Alijani * Pages 165-177
    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.
    Keywords: Dual frame, Equivalent ?-frame, Frame operator, ?-frame, Operator dual frame
  • Roghaye Jalal Shahkoohi, Zohreh Bagheri* Pages 179-212
    In 2014, Zead Mustafa introduced b2 -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 b2-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered b2-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 (ψ,φ)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 b2 -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.
    Keywords: Fixed point, Complete metric space, Ordered b2-metric space
  • Hadis Pazandeh, Davood Alimohammadi * Pages 213-240
    In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry T:A⟶B , where A and B are complex function spaces on compact Hausdorff spaces X and Y, respectively, whenever ER(A,X)=Ch(A,X) and ER(B,Y)=Ch(B,Y). Next, we give a description of T whenever A and B are complex function algebras and T does not assume to be unit-preserving.
    Keywords: Choquet boundary, Function algebra, Function space, Real-linear uniform isometry