Mostrando recursos 1 - 20 de 35

  1. Existence and Global Stability Results for Volterra Type Fractional Hadamard Partial Integral Equations

    Abbas, S.; Albarakati, W.; Benchohra, M.; Nieto, J.J.
    This paper deals with the global existence and stability of solutions of a new class of partial integral equations of Hadamard fractional order.

  2. A Simple Estimate of the Bloch Constant

    Izuki, Mitsuo; Koyama, Takeshi; Noi, Takahiro; Takeuchi, Tatsuki
    Our aim is to give a simple estimate of the Bloch constant applying some fundamental facts on complex analysis. Our method is based on the Cauchy estimate, the maximum modulus principle, the Schwarz lemma and the Rouche theorem.

  3. A Compactness Result For An Equation with Hölderian Condition

    Bahoura, Samy Skander
    We give blow-up behavior for a Brezis and Merle's problem with Dirichlet and Hölderian conditions. Also we derive a compactness criterion as in the work of Brezis and Merle.

  4. Hardy Classes and Symbols of Toeplitz Operators

    López-García, Marco; Pérez-Esteva, Salvador
    The purpose of this paper is to study functions in the unit disk $\mathbb D$ through the family of Toeplitz operators $\{T_{φdσ_{t}}\}_{t∈[0,1)}$, where $T_{φdσ_{t}}$ is the Toeplitz operator acting the Bergman space of $\mathbb D$ and where $dσ_t$ is the Lebesgue measure in the circle $tS^1$. In particular for $1\le p \lt \infty$ we characterize the harmonic functions $φ$ in the Hardy space $h^{p}(\mathbb D)$ by the growth in $t$ of the $p$-Schatten norms of $T_{φdσ_{t}}$. We also study the dependence in $t$ of the norm operator of $T_{adσ_{t}}$ when $a∈H^p_{at}$, the atomic Hardy space in the unit circle with...

  5. Derivatives on Function Spaces Generated By the Dirichlet Laplacian and the Neumann Laplacian in One Dimension

    Iwabuchi, Tsukasa
    We investigate the relation between Besov spaces generated by the Dirichlet Laplacian and the Neumann Laplacian in one space dimension from the view point of the boundary value of functions. Derivatives on spaces with such boundary conditions are defined, and it is proved that the derivative operator is isomorphic from one to the other.

  6. On the Oscillation of Solutions of First-Order Difference Equations with Delay

    Shoukaku, Y.
    Consider the first order delay difference equation $$\Delta x_{n} + p_{n} x_{\sigma(n)} = 0, \quad n \in {\mathbb N}_0,$$ where $\{p_{n}\}_{n \in {\mathbb N}_0}$ is a sequence of nonnegative real numbers, and $\{\sigma(n)\}_{n \in {\mathbb N}_0}$ is a sequence of integers such that $\sigma(n) \le n-1$, and $\displaystyle \lim_{n \to \infty}\sigma(n) = +\infty$. We obtain similar oscillation criteria of delay differential equations. This criterion is used by more simple method until now.

  7. On the Oscillation of Solutions of First-Order Difference Equations with Delay

    Shoukaku, Y.
    Consider the first order delay difference equation $$\Delta x_{n} + p_{n} x_{\sigma(n)} = 0, \quad n \in {\mathbb N}_0,$$ where $\{p_{n}\}_{n \in {\mathbb N}_0}$ is a sequence of nonnegative real numbers, and $\{\sigma(n)\}_{n \in {\mathbb N}_0}$ is a sequence of integers such that $\sigma(n) \le n-1$, and $\displaystyle \lim_{n \to \infty}\sigma(n) = +\infty$. We obtain similar oscillation criteria of delay differential equations. This criterion is used by more simple method until now.

  8. Weak Solutions for Implicit Hilfer Fractional Differential Equations With Not Instantaneous Impulses

    Abbas, S.; Benchohra, M.; Henderson, J.
    In this paper, we present results concerning the existence of weak solutions for some functional implicit Hilfer fractional differential equations with not instantaneous impulses in Banach spaces. The main results are proved by applying Mönch's fixed point theorem associated with the technique of measure of weak non compactness, and we present an illustrative example.

  9. Weak Solutions for Implicit Hilfer Fractional Differential Equations With Not Instantaneous Impulses

    Abbas, S.; Benchohra, M.; Henderson, J.
    In this paper, we present results concerning the existence of weak solutions for some functional implicit Hilfer fractional differential equations with not instantaneous impulses in Banach spaces. The main results are proved by applying Mönch's fixed point theorem associated with the technique of measure of weak non compactness, and we present an illustrative example.

  10. General Adjoint on a Banach Space

    Gill, Tepper L.
    In this paper, we show that the continuous dense embedding of a separable Banach space $\mathcal B$ into a Hilbert space $\mathcal H$ offers a new tool for studying the structure of operators on a Banach space. We use this embedding to demonstrate that the dual of a Banach space is not unique. As a application, we consider this non-uniqueness within the $\mathbb C[0,1] \subset L^2[0,1]$ setting. We then extend our theory every separable Banach space $\mathcal B$. In particular, we show that every closed densely defined linear operator $A$ on $\mathcal B$ has a unique adjoint $A^*$ defined on...

  11. General Adjoint on a Banach Space

    Gill, Tepper L.
    In this paper, we show that the continuous dense embedding of a separable Banach space $\mathcal B$ into a Hilbert space $\mathcal H$ offers a new tool for studying the structure of operators on a Banach space. We use this embedding to demonstrate that the dual of a Banach space is not unique. As a application, we consider this non-uniqueness within the $\mathbb C[0,1] \subset L^2[0,1]$ setting. We then extend our theory every separable Banach space $\mathcal B$. In particular, we show that every closed densely defined linear operator $A$ on $\mathcal B$ has a unique adjoint $A^*$ defined on...

  12. General Adjoint on a Banach Space

    Gill, Tepper L.
    In this paper, we show that the continuous dense embedding of a separable Banach space $\mathcal B$ into a Hilbert space $\mathcal H$ offers a new tool for studying the structure of operators on a Banach space. We use this embedding to demonstrate that the dual of a Banach space is not unique. As a application, we consider this non-uniqueness within the $\mathbb C[0,1] \subset L^2[0,1]$ setting. We then extend our theory every separable Banach space $\mathcal B$. In particular, we show that every closed densely defined linear operator $A$ on $\mathcal B$ has a unique adjoint $A^*$ defined on...

  13. General Adjoint on a Banach Space

    Gill, Tepper L.
    In this paper, we show that the continuous dense embedding of a separable Banach space $\mathcal B$ into a Hilbert space $\mathcal H$ offers a new tool for studying the structure of operators on a Banach space. We use this embedding to demonstrate that the dual of a Banach space is not unique. As a application, we consider this non-uniqueness within the $\mathbb C[0,1] \subset L^2[0,1]$ setting. We then extend our theory every separable Banach space $\mathcal B$. In particular, we show that every closed densely defined linear operator $A$ on $\mathcal B$ has a unique adjoint $A^*$ defined on...

  14. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...

  15. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...

  16. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...

  17. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...

  18. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...

  19. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...

  20. Norm Estimates for Powers of Products of Operators in a Banach Space

    Gil’, Michael
    Let $A$ and $B$ be bounded linear operators in a Banach space. We consider the following problem: if $\Sigma_{k=0}^{\infty} || A^{k} |||| B^{k} || \lt\infty$, under what conditions $\Sigma_{k=0}^{\infty} || (AB)^{k} || \lt \infty$?

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