Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2022-10-31

    Certain image formulas of $(p,\nu)$--extended Gauss' hypergeometric function and related Jacobi transforms

    Purnima Chopra, Mamta Gupta, Kanak Modi

    Abstract : Our aim is to establish certain image formulas of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erd\'elyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the $ (p,\nu)$--extended Gauss's hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$. We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$.

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  • 2022-04-30

    Double series transforms derived from Fourier--Legendre theory

    John Maxwell Campbell, Wenchang Chu

    Abstract : We apply Fourier--Legendre-based integration methods that had been given by Campbell in 2021, to evaluate new rational double hypergeometric sums involving $frac{1}{pi}$. Closed-form evaluations for dilogarithmic expressions are key to our proofs of these results. The single sums obtained from our double series are either inevaluable ${}_{2}F_{1}( frac45 )$- or ${}_{2}F_{1}( frac12 )$-series, or Ramanujan's ${}_{3}F_{2}(1)$-series for the moments of the complete elliptic integral $ ext{{f K}}$. Furthermore, we make use of Ramanujan's finite sum identity for the aforementioned ${}_{3}F_{2}(1)$-family to construct creative new proofs of Landau's asymptotic formula for the Landau constants.

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  • 2022-01-31

    Hermite-type exponentially fitted interpolation formulas using three unequally spaced nodes

    Kyung Joong Kim

    Abstract : Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an $omega$-dependent function $f$ but also the values of its first derivative at three unequally spaced nodes. The function $f$ is of the form, egin{equation*} egin{array}{ccc} f(x) = g_1(x) cos (omega x) + g_2(x) sin (omega x), ,, x in [a, b], end{array} end{equation*} where $g_1$ and $g_2$ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas $I_N$ built on the foundation using $N$ unequally spaced nodes. Then the coefficients of $I_N$ are determined by solving a linear system, and some of the properties of these coefficients are obtained. When $N$ is $2$ or $3,$ some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with $I_N.$ For $N=3,$ the errors for $I_N$ are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

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  • 2022-10-31

    Golden para-contact metric manifolds

    Gherici Beldjilali, Habib Bouzir

    Abstract : The purpose of the present paper is to introduce a new class of almost para-contact metric manifolds namely, Golden para-contact metric manifolds. Then, we are particularly interested in a more special type called Golden para-Sasakian manifolds, where we will study their fundamental properties and we present many examples which justify their study.

  • 2022-01-31

    On an integral involving ={I}-function

    Vilma D'Souza, Shantha Kumari Kurumujji

    Abstract : In this paper, an interesting integral involving the ={I}-function of one variable introduced by Rathie has been derived. Since ={I}-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the ={I} function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

  • 2023-01-31

    An exponentially fitted method for two parameter singularly perturbed parabolic boundary value problems

    Gemechis File Duressa, Tariku Birabasa Mekonnen

    Abstract : This article devises an exponentially fitted method for the numerical solution of two parameter singularly perturbed parabolic boundary value problems. The proposed scheme is able to resolve the two lateral boundary layers of the solution. Error estimates show that the constructed scheme is parameter-uniformly convergent with a quadratic numerical rate of convergence. Some numerical test examples are taken from recently published articles to confirm the theoretical results and demonstrate a good performance of the current scheme.

  • 2022-04-30

    $f$-biharmonic submanifolds and $f$-biharmonic integral submanifolds in locally conformal almost cosymplectic space forms

    Mohd Aslam, Fatma Karaca, Aliya Naaz Siddiqui

    Abstract : In this paper, we have studied $f$-biharmonic submanifolds in locally conformal almost cosymplectic space forms and have derived condition on second fundamental form for $f$-biharmonic submanifolds. Also, we have discussed its integral submanifolds in locally conformal almost cosymplectic space forms.

  • 2023-04-30

    Unitary analogues of a generalized number-theoretic sum

    Traiwat Intarawong, Boonrod Yuttanan

    Abstract : In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.

  • 2022-04-30

    Almost weakly finite conductor rings and weakly finite conductor rings

    Hanan Choulli, Haitham El Alaoui, Hakima Mouanis

    Abstract : Let $R$ be a commutative ring with identity. We call the ring $R$ to be an almost weakly finite conductor if for any two elements $a$ and $b$ in $R$, there exists a positive integer $n$ such that $a^{n}Rcap b^{n}R$ is finitely generated. In this article, we give some conditions for the trivial ring extensions and the amalgamated algebras to be almost weakly finite conductor rings. We investigate the transfer of these properties to trivial ring extensions and amalgamation of rings. Our results generate examples which enrich the current literature with new families of examples of non-finite conductor weakly finite conductor rings.

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  • 2023-04-30

    The measurability of Hewitt-Stromberg measures and dimensions

    Zied Douzi, Bilel Selmi, Haythem Zyoudi

    Abstract : The aim of this paper is to study the descriptive set-theoretic complexity of the Hewitt-Stromberg measure and dimension maps.

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October, 2023
Vol.38 No.4

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