فهرست مطالب

Sahand Communications in Mathematical Analysis - Volume:9 Issue: 1, 2018
  • Volume:9 Issue: 1, 2018
  • تاریخ انتشار: 1396/11/20
  • تعداد عناوین: 8
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  • Maliheh Mayghani, Davood Alimohammadi Pages 1-14
    We first show that a bounded linear operator T on a real Banach space E is quasicompact (Riesz, respectively) if and only if T ′ :E C ⟶E C is quasicompact (Riesz, respectively), where the complex Banach space EC is a suitable complexification of E and T ′ is the complex linear operator on EC associated with T . Next, we prove that every unital endomorphism of real Lipschitz algebras of complex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Finally, we study some properties of quasicompact and Riesz unital endomorphisms of these algebras.
    Keywords: Complexification, Lipschitz algebra, Lipschitz involution, Quasicompact operator, Riesz operator, Unital endomorphism
  • Telman Gasymov, Chingiz Hashimov Pages 15-32
    An atomic decomposition is considered in Banach space. A method for constructing an atomic decomposition of Banach space, starting with atomic decomposition of subspaces is presented. Some relations between them are established. The proposed method is used in the study of the frame properties of systems of eigenfunctions and associated functions of discontinuous differential operators.
    Keywords: p -frames, tildeX -frames, Conjugate systems to tildeX
  • Elham Bayatmanesh, Mohammad Akbari Tootkaboni Pages 33-43
    Let S be a dense subsemigroup of (0,∞) . In this paper, we state definition of thick near zero, and also we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman and Leader in [6]. We define density near zero for subsets of S by a collection of nonempty finite subsets of S and we investigate the conditions under these concepts.
    Keywords: The Stone-Cech compactification, Density, Piecewise syndetic set near zero
  • Mahdi Nazarianpoor, Ghadir Sadeghi Pages 45-83
    In this paper, we investigate the Hyers-Ulam stability of the orthogonally cubic equation and Pexiderized cubic equation
    f(kx)(kx−y)=g(x)(x−y) g(kx)−2g(x),
    f(kx)(kx−y)=g(x)(x−y)�(kx)−2g(x),
    in multi-normed spaces by the direct method and the fixed point method. Moreover, we prove the Hyers-Ulam stability of the 2 -variables cubic equation
    f(2x,2z)(2x−y,2z−t)=2f(x,z)(x−y,z−t)흧(x,z),
    f(2x,2z)(2x−y,2z−t)=2f(x,z)(x−y,z−t)흧(x,z),
    and orthogonally cubic type and k -cubic equation in multi-normed spaces. A counter example for non stability of the cubic equation is also discussed.
    Keywords: Hyers-Ulam stability, Multi-normed space, Cubic functional equation, Pexiderized cubic functional equation, 2 -variables cubic functional equation
  • Mohadeseh Paknazar Pages 85-112
    In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the usability of the obtained results.
    Keywords: Fuzzy metric space, Best proximity point, Proximal contraction
  • Ghorbanali Haghighatdoost, Hami Abbasi Makrani, Rasoul Mahjoubi Pages 113-128
    In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple (R,H,X) consisting of a regular multiplier Hopf algebra H , a left H -comodule algebra R , and a unital left H -module X which is also a unital algebra. First, we construct a paracyclic module to a triple (R,H,X) and then prove the existence of a cyclic structure associated to this triple.
    Keywords: Multiplier Hopf algebra, Cyclic homology, Cyclic module, Paracyclic module, H− comodule
  • Mehdi Rashidi-Kouchi Pages 129-142
    In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.
    Keywords: Super Hilbert_Frame_G-Frame_Hilbert C ∗ -module
  • Ali Hassanzadeh, Ildar Sadeqi Pages 143-150
    In this paper, a Krein-Milman type theorem in T0 semitopological cone is proved, in general. In fact, it is shown that in any locally convex T0 semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.
    Keywords: T0 topology, Extreme Point, Krein-Milman type theorem