• Title/Summary/Keyword: Mean value theorem

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A STUDY OF THE RIGHT LOCAL GENERAL TRUNCATED M-FRACTIONAL DERIVATIVE

  • Chauhan, Rajendrakumar B.;Chudasama, Meera H.
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.503-520
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    • 2022
  • We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.

ACCESS TO LAPLACE TRANSFORM OF fg

  • HWAJOON KIM;SOMCHAI LEKCHAROEN
    • Journal of applied mathematics & informatics
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    • v.41 no.1
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    • pp.83-93
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    • 2023
  • We would like to consider Laplace transform of the form of fg, the form of product, and applies it to Burger's equation in general case. This topic has not yet been addressed, and the methodology of this article is done by considerations with respect to several approaches about the transform of the form of f g and the mean value theorem for integrals. This paper has meaning in that the integral transform method is applied to solving nonlinear equations.

ON THE HYBRID MEAN VALUE OF GENERALIZED DEDEKIND SUMS, GENERALIZED HARDY SUMS AND KLOOSTERMAN SUMS

  • Qing Tian;Yan Wang
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.611-622
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    • 2023
  • The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.

A Study on the Ionogram Inversion Algorithm Using Mean Value Theorem (평균치 정리를 이용한 진리층관측도 변환 알고리즘에 관한 연구)

  • Park, Hyung Rae;Chae, Jong Seok;Lee, Hyuck Jae
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.24 no.2
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    • pp.201-206
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    • 1987
  • A description of ionogram inversion algorithm developed for obtaining ionospheric electron density profile from ionospheric sounding datas (ionograms) in real time using mean value theorem is given and the methods for determining starting points and correcting valley effects are considered. The results derived from this algorithm are compared with the theoretically simulated datas, and the real electron density profiles from the measured ionograms taken at Radio research Laboratory in Korea are given to show its practical use.

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MEAN-VALUE PROPERTY AND CHARACTERIZATIONS OF SOME ELEMENTARY FUNCTIONS

  • Matkowski, Janusz
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.263-273
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    • 2013
  • A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

Likely Mean Value Theorem

  • Choi, J.R.;Ha, H.Y.;Kwun, Y.C.;Nam, H.I.
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1997.11a
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    • pp.37-42
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    • 1997
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A NEW MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND KLOOSTERMAN SUMS

  • Han, Di;Zhang, Wenpeng
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.35-43
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    • 2015
  • Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.