• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.899-911
• /
• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• Kyungpook Mathematical Journal
• /
• v.48 no.2
• /
• pp.165-171
• /
• 2008

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.259-275
• /
• 2019

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.277-303
• /
• 2021

Under the rough kernels Ω belonging to the block spaces B0,qr (Sn-1) or the radial Grafakos-Stefanov kernels W����(Sn-1) for some r, �� > 1 and q ≤ 0, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in [27, 28], in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class L(log L)α(Sn-1) or the Grafakos-Stefanov class ����(Sn-1) for some α ∈ [0, 1] and �� ∈ (2, ∞).

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.2
• /
• pp.537-555
• /
• 2023

In this paper, we consider two types of fractional boundary value problems, one of them is an implicit type and the other will be an integro-differential type with nonlocal integral multi-point boundary conditions in the frame of generalized Hilfer fractional derivatives. The existence and uniqueness results are acquired by applying Krasnoselskii's and Banach's fixed point theorems. Some various numerical examples are provided to illustrate and validate our results. Moreover, we get some results in the literature as a special case of our current results.

• Proceedings of the KIEE Conference
• /
• 1991.07a
• /
• pp.657-665
• /
• 1991

Although orthogonal function is introduced in control theory in early 1970's, it is not perfect. Since the concept of integral operator by Chen and Hsiao in mid 1970's, orthogonal function (for example Walsh, Block-pulse, Haar, Laguerre, Legendre, Chebychev etc) has been widely applied In system's analysis and identification, model reduction, state estimation, optimal control, signal processing, image processing, EEG, and ECG etc. The reason why Walsh Functions introduces in control theory is that as integral of Walsh function is also developed in Walsh orthogonal function, if we transfer give system into integral equation and introduce Walsh function. We can know that system's characteristic by algebraical expression. This approach is based on least square error and that result is expressed as computer calculation and partly continuous constant value which is easy to apply. Such a Walsh function has been actively studied in USA, TAIWAN, INDO, CHINA, EUROPE etc and in domestic, author has studied it for 10 years since it was is introduced in 1982. This paper is consider the that author has studied for 10 years and Walsh function's efficiency.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.135-146
• /
• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.4
• /
• pp.383-391
• /
• 2006

A characterization of Gaussian process with independent increments in terms of the support of covariance operator is established. We investigate the Girsanov formula for a Gaussian process with independent increments.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.399-410
• /
• 2003

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions in the open unit disk defined by multiplier transformations and study their properties. Our results include several previous known results as special cases.

• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.575-585
• /
• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.