فهرست مطالب

Mathematical Extension - Volume:16 Issue: 2, Feb 2022

Journal of Mathematical Extension
Volume:16 Issue: 2, Feb 2022

  • تاریخ انتشار: 1400/04/17
  • تعداد عناوین: 6
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  • Z. S. Mirsaney, M. Rezaei∗ Page 1

    Results concerning local boundedness of operators have a long history. In 1994, Vesely connected the concept of approximate ´ monotonicity of an operator with local boundedness of that. It is our desire in this note to characterize an approximate monotone operator. Actually, we show that a well-known property of monotone operators, namely representing by convex functions, remains valid for the larger subclass of operators. In this general framework we establish the similar results by Fitzpatrick. Also, celebrated results of Mart´inez-Legaz and Th´era inspired us to prove that the set of maximal ε-monotone operators between a normed linear space X and its continuous dual X ∗ can be identified as some subset of convex functions on X × X ∗ .

    Keywords: θ′-monotone, θ-Fitzpatrick function, convex, θ-subdifferential, maximal θ′-monotone, θ′-conjugate
  • H. Mahzoon* Page 2

    Let α ∈ [π/2, π) and γ1, γ2 ∈ (0, 1]. For a normalized analytic functions f in the open unit disc ∆ we consider M(α) := { f ∈ A : 1 + α − π 2 sin α < Re { zf′ (z) f(z) } < 1 + α 2 sin α , z ∈ ∆ } , and S ∗ t (γ1, γ2) := { f ∈ A : − πγ1 2 < arg { zf′ (z) f(z) } < πγ2 2 , z ∈ ∆ } . In the present paper, we establish a sharp norm estimate of the pre– Schwarzian derivative for functions f belonging two these subclasses of analytic and normalized functions.

    Keywords: Univalent, starlike, locally univalent, subordination, pre-Schwarzian norm
  • Sanaz Asadi Rahmati, Reza Fallahnejad* Page 3

    Data Envelopment Analysis(DEA) is a non-parametric method for evaluating the efficiency of those Decision Making Units (DMUs) that have the same functionality and use multiple inputs to generate multiple outputs‎. ‎DMUs may sometimes be divided into several groups according to a series of criteria‎, ‎and it is intended to evaluate a group of similar DMUs‎. ‎In this paper‎, ‎each group was considered as a player in a cooperative game and a subset of groups was considered as a coalition‎. ‎Assuming the Production Possibility Set is made up of the members of the coalition‎, ‎a characteristic function was defined in terms of the sum of the efficiency of all units to determine the marginal effect of each group in different coalitions‎. ‎The groups were then evaluated using the Shapley Value as a solution of the cooperative game‎. ‎Some Examples were provided to describe and apply the method‎.

    Keywords: Data envelopment analysis (DEA)‎, ‎Group evaluation‎, ‎Game theory‎, ‎Cooperative game‎, ‎Shapley Value‎
  • Y. Sohooli, K. Jahedi*, A. Alikhani-Koopaei Page 4

    The aim of this paper is to introduce an equivalence relation on the space of real valued statistically convergence sequences, Cst, and an inner product on the set of its equivalence classes. We equip Cst with the induced J- metric, dJ , by the given inner product. We prove that Cst is a complete J-metric space. We also show that the space of all real valued convergent sequences is a dense subspace of (Cst, dJ ).

    Keywords: Natural density of sets, statistically convergence, equivalence relation, quotient space
  • T. Prasad* Page 5

    In this paper, we study coposinormal composition operators and posinormal weighted composition operators on the Hardy space H2 (D). We show that if Wψ,ϕ is coposinormal on H2 (D), then ψ never vanishes on D also we prove that ϕ is univalent. Moreover, we study the commutant of a coposinormal weighted composition operator.

    Keywords: posinormal operator, composition operator, cyclic operator, Toeplitz operator, Hardy space
  • J. Khazaeian, N. Parandin*, F. Mohammadi Yaghoobi, N. Karamikabir Page 6

    In this paper, an iterative method is extended to solve nonlinear two- and three-dimensional mixed Volterra-Fredholm integral equations. We consider a nonlinear operator of these integral equations and then develop the iterative method which was introduced in [J MATH ANAL APPL. 316 (2006) 753-763] to solve them. Convergence property of the suggested schemes are proved under some mild assumptions. In both cases, numerical examples are given to compare the performance of the proposed method with some existing methods.

    Keywords: Nonlinear mixed Volterra-Fredholm integralequations, Iterative method, Banach fixed point theorem, Numericalsolution