• Title/Summary/Keyword: integral operator.

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ORLICZ-TYPE INTEGRAL INEQUALITIES FOR OPERATORS

  • Neugebauer, C.J.
    • Journal of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.163-176
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    • 2001
  • We examine Orlicz-type integral inequalities for operators and obtain as a corollary a characterization of such inequalities for the Hardy-Littlewood maximal operator extending the well-known L(sup)p-norm inequalities.

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OPERATOR-VALUED FUNCTION SPACE INTEGRALS VIA CONDITIONAL INTEGRALS ON AN ANALOGUE WIENER SPACE II

  • Cho, Dong Hyun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.903-924
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    • 2016
  • In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

HYPONORMAL SINGULAR INTEGRAL OPERATORS WITH CAUCHY KERNEL ON L2

  • Nakazi, Takahiko
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.787-798
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    • 2018
  • For $1{\leq}p{\leq}{\infty}$, let $H^p$ be the usual Hardy space on the unit circle. When ${\alpha}$ and ${\beta}$ are bounded functions, a singular integral operator $S_{{\alpha},{\beta}}$ is defined as the following: $S_{{\alpha},{\beta}}(f+{\bar{g}})={\alpha}f+{\beta}{\bar{g}}(f{\in}H^p,\;g{\in}zH^p)$. When p = 2, we study the hyponormality of $S_{{\alpha},{\beta}}$ when ${\alpha}$ and ${\beta}$ are some special functions.

ON THE q-EXTENSION OF THE HARDY-LITTLEWOOD-TYPE MAXIMAL OPERATOR RELATED TO q-VOLKENBORN INTEGRAL IN THE p-ADIC INTEGER RING

  • Jang, Lee-Chae
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.207-213
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    • 2010
  • In this paper, we define the q-extension of the Hardy-Littlewood-type maximal operator related to q-Volkenborn integral. By the meaning of the extension of q-Volkenborn integral, we obtain the boundedness of the q-extension of the Hardy-Littlewood-type maximal operator in the p-adic integer ring.

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

  • Akgul, Arzu
    • Honam Mathematical Journal
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    • v.39 no.3
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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.

SOME PROPERTIES FOR SPIRALLIKE FUNCTIONS INVOLVING GENERALIZED q-INTEGRAL OPERATOR

  • Sahsene Altinkaya;Asena Cetinkaya
    • Honam Mathematical Journal
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    • v.45 no.4
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    • pp.689-700
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    • 2023
  • In this note, we establish a new subfamily of spirallike functions by making use of a generalized q-integral operator. We examine characterization rule for functions which are member of this subclass. We further obtain coefficient estimate, subordination results and integral mean inequalities for functions in this class. The Fekete-Szegö inequalities are also derived.

SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY LOMMEL OPERATOR

  • Altinkaya, Sahsene;Badar, Rizwan Salim;Noor, Khalida Inayat
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.567-574
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    • 2022
  • We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

SPECTRAL ANALYSIS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION I: POSITIVENESS AND CONTRACTIVENESS

  • Choi, Sung-Woo
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.27-47
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    • 2012
  • It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.

BOUNDS OF AN INTEGRAL OPERATOR FOR CONVEX FUNCTIONS AND RESULTS IN FRACTIONAL CALCULUS

  • Mishira, Lakshmi Narayan;Farid, Ghulam;Bangash, Babar Khan
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.359-376
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    • 2020
  • The present research investigates the bounds of an integral operator for convex functions and a differentiable function f such that |f'| is convex. Further, these bounds of integral operators specifically produce estimations of various classical fractional and recently defined conformable integral operators. These results also contain bounds of Hadamard type for symmetric convex functions.