• Title, Summary, Keyword: integral operators

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SANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS

  • Cho, Nak-Eun
    • East Asian mathematical journal
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    • v.28 no.3
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    • pp.321-332
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    • 2012
  • The purpose of the present paper is to investigate some subordination and superordination preserving properties of certain integral operators de ned on the space of meromorphic functions in the puncture open unit disk. The sandwich-type theorems for these integral operators are also presented.

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.

Properties of integral operators in complex variable boundary integral equation in plane elasticity

  • Chen, Y.Z.;Wang, Z.X.
    • Structural Engineering and Mechanics
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    • v.45 no.4
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    • pp.495-519
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    • 2013
  • This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

THE (k, s)-FRACTIONAL CALCULUS OF CLASS OF A FUNCTION

  • Rahman, G.;Ghaffar, A.;Nisar, K.S.;Azeema, Azeema
    • Honam Mathematical Journal
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    • v.40 no.1
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    • pp.125-138
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    • 2018
  • In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

ON C-STIELTJES INTEGRAL OF BANACH-VALVED FUNCTIONS

  • Zhang, Xiaojie;Zhao, Dafang;Ye, Guoju
    • The Pure and Applied Mathematics
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    • v.14 no.2
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    • pp.71-84
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    • 2007
  • In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.

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INTEGRAL KERNEL OPERATORS ON REGULAR GENERALIZED WHITE NOISE FUNCTIONS

  • Ji, Un-Cig
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.601-618
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    • 2000
  • Let (and $g^*$) be the space of regular test (and generalized, resp.) white noise functions. The integral kernel operators acting on and transformation groups of operators on are studied, and then every integral kernel operator acting on can be extended to continuous linear operator on $g^*$. The existence and uniqueness of solutions of Cauchy problems associated with certain integral kernel operators with intial data in $g^*$ are investigated.

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Invariance of the space of theta-series under theta operators

  • Kim, Myung-Hwan
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.245-256
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    • 1992
  • In this article, we study the behavior of half integral weight thetaseries under theta operators. Theta operators are very important in the study of theta-series in connection with Hecke operators. Andrianov[A1] proved that the space of integral weight theta-series is invariant under the action of theta operators. We prove that his statement can be extened for half integral weight theta-series with a slight modification. By using this result one can prove that the space of theta-series is invariant under the action of Hecke operators as Andrianov did for intrgral weight theta-series [A1].

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INTEGRAL REPRESENTATIONS IN ELECTRICAL IMPEDANCE TOMOGRAPHY USING BOUNDARY INTEGRAL OPERATORS

  • Kwon, Ki-Woon
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.97-119
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    • 2008
  • Electrical impedance tomography (EIT) problem with anisotropic anomalous region is formulated in a few different ways using boundary integral operators. The Frechet derivative of Neumann-to-Dirichlet map is computed also by using boundary integral operators and the boundary of the anomalous region is approximated by trigonometric expansion with Lagrangian basis. The numerical reconstruction is done in case that the conductivity of the anomalous region is isotropic.