• 제목/요약/키워드: operator condition

검색결과 462건 처리시간 0.022초

ON THE INVERSE PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH A NONLINEAR SPECTRAL PARAMETER IN THE BOUNDARY CONDITION

  • Mamedov, Khanlar R.
    • 대한수학회지
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    • 제46권6호
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    • pp.1243-1254
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    • 2009
  • The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, $\infty$). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

ITERATION PROCESSES WITH ERRORS FOR NONLINEAR EQUATIONS INVOLVING $\alpha$-STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES

  • Jung, Jong-Soo
    • East Asian mathematical journal
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    • 제17권2호
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    • pp.349-365
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    • 2001
  • Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.

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On Normal Products of Selfadjoint Operators

  • Jung, Il Bong;Mortad, Mohammed Hichem;Stochel, Jan
    • Kyungpook Mathematical Journal
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    • 제57권3호
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    • pp.457-471
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    • 2017
  • A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A, B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.

ANALYTIC FUNCTIONS WITH CONIC DOMAINS ASSOCIATED WITH CERTAIN GENERALIZED q-INTEGRAL OPERATOR

  • Om P. Ahuja;Asena Cetinkaya;Naveen Kumar Jain
    • 대한수학회논문집
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    • 제38권4호
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    • pp.1111-1126
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    • 2023
  • In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

FRACTIONAL ORDER OF DIFFERENTIAL INCLUSION GOVERNED BY AN INVERSE STRONGLY AND MAXIMAL MONOTONE OPERATOR

  • Aicha Ouali;Abdallah Beddani;Yamina Miloudi
    • Nonlinear Functional Analysis and Applications
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    • 제29권3호
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    • pp.739-751
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    • 2024
  • In this paper, we study the existence and uniqueness of solutions for a class of fractional differential inclusion including a maximal monotone operator in real space with an initial condition. The main results of the existence and uniqueness are obtained by using resolvent operator techniques and multivalued fixed point theory.

ON SIMILARITY AND REDUCING SUBSPACES OF A CLASS OF OPERATOR ON THE DIRICHLET SPACE

  • Caixing Gu;Yucheng Li;Hexin Zhang
    • 대한수학회보
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    • 제61권4호
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    • pp.949-957
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    • 2024
  • Let Yp be the multiplication operator Mp plus the Volterra operator Vp induced by p(z), where p is a polynomial. Under a mild condition, we prove that Yp acting on the Dirichlet space 𝔇 is similar to multiplication operator Mp acting on a subspace S(𝔻) of 𝔇. Furthermore, it shows that Tzn (n ≥ 2) has exactly 2n reducing subspaces on 𝔇.

Three Characteristic Beltrami System in Even Dimensions (I): p-Harmonic Equation

  • Gao, Hongya;Chu, Yuming;Sun, Lanxiang
    • Kyungpook Mathematical Journal
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    • 제47권3호
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    • pp.311-322
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    • 2007
  • This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

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RANDOM FIXED POINT THEOREMS FOR CARISTI TYPE RANDOM OPERATORS

  • Beg, Ismat;Abbas, Mujahid
    • Journal of applied mathematics & informatics
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    • 제25권1_2호
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    • pp.425-434
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    • 2007
  • We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.

A CERTAIN SUBCLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS ASSOCIATED WITH AN INTEGRAL OPERATOR

  • Akgul, Arzu
    • 호남수학학술지
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    • 제39권3호
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    • pp.331-347
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    • 2017
  • The aim of the present paper is to introduce a new subclass of meromorphic functions with positive coefficients defined by a certain integral operator and a necessary and sufficient condition for a function f to be in this class. We obtain coefficient inequality, meromorphically radii of close-to-convexity, starlikeness and convexity, convex linear combinations, Hadamard product and integral transformation for the functions f in this class.

𝓐-Frequent Hypercyclicity in an Algebra of Operators

  • Ahn, Ka Kyung
    • 통합자연과학논문집
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    • 제10권2호
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    • pp.115-118
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    • 2017
  • We study a notion of $\mathcal{A}$-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We prove a sufficient condition for a linear map to satisfy the $\mathcal{A}$-frequent hypercyclicity in the strong operator topology.