• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.1-14
• /
• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.107-118
• /
• 2017

In this paper we study CR-submanifolds of maximal CR-dimension by investigating extrinsic behaviors of integral curves of characteristic vector field on them. Also we consider the notion of ruled CR-submanifold of maximal CR-dimension which is a generalization of that of ruled real hypersurface and find some characterizations of ruled CR-submanifold of maximal CR-dimension concerning extrinsic shapes of integral curves of the characteristic vector field and those of CR-Frenet curves.

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.155-166
• /
• 2009

We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform $\hat{F}_{{\alpha},{\beta}}F(x)$ which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in $L_2(C_0[0,T])$.

• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1171-1184
• /
• 2020

This paper presents several fractional generalizations and extensions of known integral inequalities. To obtain these, an extended generalized Mittag-Leffler function and its fractional integral operator are used.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.383-391
• /
• 2011

In this paper, we investigate some properties of the $M_{\alpha}$-integral and prove convergence theorems for the $M_{\alpha}$-integral.

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.207-212
• /
• 2022

In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-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 Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.22 no.3
• /
• pp.695-703
• /
• 1998

The crack problem of continuous casting slab due to the thermal stresses during the reheating process is analyzed using FEM. In this study, the C(t)-integral is calculated. As a result, the values of the C(t)-integral decrease by increasing the initial temperature of the slab and decreasing total heat flux. And those decrease by decreasing the heat flux of pre-heating zone and increasing the heat flux of heating zone.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.609-631
• /
• 2021

Let C[0, T] denote a generalized analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. Define $Z_{\vec{e},n}$ : C[0, T] → ℝⁿ⁺¹ by $$Z_{\vec{e},n}(x)=\(x(0),\;{\int}_0^T\;e_1(t)dx(t),{\cdots},\;{\int}_0^T\;e_n(t)dx(t)\)$$, where e₁,…, e_n are of bounded variations on [0, T]. In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function $Z_{\vec{e},n}$ which has an initial weight and a kind of drift. As applications of the formula, we evaluate the Radon-Nikodym derivatives of various functions on C[0, T] which are of interested in Feynman integration theory and quantum mechanics. This work generalizes and simplifies the existing results, that is, the simple formulas with the conditioning functions related to the partitions of time interval [0, T].

• Korean Journal of Mathematics
• /
• v.29 no.4
• /
• pp.775-784
• /
• 2021

For the polynomial P(z) of degree n and having all its zeros in |z| ≤ k, k ≥ 1, Jain [6] proved that $${{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}P^{\prime}(z){\mid}{\geq}n\;{\frac{{\mid}c_0{\mid}+{\mid}c_n{\mid}k^{n+1}}{{\mid}c_0{\mid}(1+k^{n+1})+{\mid}c_n{\mid}(k^{n+1}+k^{2n})}\;{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}P(z){\mid}$$. In this paper, we extend above inequality to its integral analogous and there by obtain more results which extended the already proved results to integral analogous.

• Korean Journal of Mathematics
• /
• v.28 no.1
• /
• pp.17-30
• /
• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.