• 제목/요약/키워드: integral operators

검색결과 217건 처리시간 0.021초

BOUNDEDNESS OF 𝓒b,c OPERATORS ON BLOCH SPACES

  • Nath, Pankaj Kumar;Naik, Sunanda
    • Korean Journal of Mathematics
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    • 제30권3호
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    • pp.467-474
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    • 2022
  • In this article, we consider the integral operator 𝓒b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒b,c operators on Bloch spaces.

SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION

  • Rao, Snehal B.;Patel, Amit D.;Prajapati, Jyotindra C.;Shukla, Ajay K.
    • 대한수학회논문집
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    • 제28권2호
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    • pp.303-317
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    • 2013
  • In present paper, we obtain functions $R_t(c,{\nu},a,b)$ and $R_t(c,-{\mu},a,b)$ by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function $_2R_1(a,b;c;{\tau};z)$ and some special cases have also been discussed.

HYPONORMAL SINGULAR INTEGRAL OPERATORS WITH CAUCHY KERNEL ON L2

  • Nakazi, Takahiko
    • 대한수학회논문집
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    • 제33권3호
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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.

FRACTIONAL CALCULUS AND INTEGRAL TRANSFORMS OF INCOMPLETE τ-HYPERGEOMETRIC FUNCTION

  • Pandey, Neelam;Patel, Jai Prakash
    • 대한수학회논문집
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    • 제33권1호
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    • pp.127-142
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    • 2018
  • In the present article, authors obtained certain fractional derivative and integral formulas involving incomplete ${\tau}$-hypergeometric function introduced by Parmar and Saxena [14]. Some interesting special cases and consequences of our main results are also considered.

SOME PROPERTIES OF GENERALIZED BESSEL FUNCTION ASSOCIATED WITH GENERALIZED FRACTIONAL CALCULUS OPERATORS

  • Jana, Ranjan Kumar;Pal, Ankit;Shukla, Ajay Kumar
    • 대한수학회논문집
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    • 제36권1호
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    • pp.41-50
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    • 2021
  • This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

  • Jang, Lee-Chae
    • 호남수학학술지
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    • 제30권1호
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    • pp.171-183
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    • 2008
  • In a previous work [18], the authors investigated autocontinuity, converse-autocontinuity, uniformly autocontinuity, uniformly converse-autocontinuity, and fuzzy multiplicativity of monotone set function defined by Choquet integral([3,4,13,14,15]) instead of fuzzy integral([16,17]). We consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [18]. These integrals, which can be regarded as interval-valued aggregation operators, have been used in [10,11,12,19,20]. In this paper, we investigate some characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral such as autocontinuity, converse-autocontinuity, uniform autocontinuity, uniform converse-autocontinuity, and fuzzy multiplicativity.

SOME FAMILIES OF INFINITE SERIES SUMMABLE VIA FRACTIONAL CALCULUS OPERATORS

  • Tu, Shih-Tong;Wang, Pin-Yu;Srivastava, H.M.
    • East Asian mathematical journal
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    • 제18권1호
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    • pp.111-125
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    • 2002
  • Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

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SOME PROPERTIES OF CERTAIN CLASSES OF FUNCTIONS WITH BOUNDED RADIUS ROTATIONS

  • NOOR, KHALIDA INAYAT
    • 호남수학학술지
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    • 제19권1호
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    • pp.97-105
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    • 1997
  • Let $R_k({\alpha})$, $0{\leq}{\alpha}<1$, $k{\geq}2$ denote certain subclasses of analytic functions in the unit disc E with bounded radius rotation. A function f, analytic in E and given by $f(z)=z+{\sum_{m=2}^{\infty}}a_m{z^m}$, is said to be in the family $R_k(n,{\alpha})n{\in}N_o=\{0,1,2,{\cdots}\}$ and * denotes the Hadamard product. The classes $R_k(n,{\alpha})$ are investigated and same properties are given. It is shown that $R_k(n+1,{\alpha}){\subset}R_k(n,{\alpha})$ for each n. Some integral operators defined on $R_k(n,{\alpha})$ are also studied.

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