• 호남수학학술지
• /
• 제45권1호
• /
• pp.54-70
• /
• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• Journal of applied mathematics & informatics
• /
• 제32권1_2호
• /
• pp.247-254
• /
• 2014

In this paper, we investigate bounds for solutions of nonlinear perturbed differential systems.

• 충청수학회지
• /
• 제28권1호
• /
• pp.73-82
• /
• 2015

In this paper, we investigate h-stability and bounds for solutions of the the functional perturbed differential systems

• 대한수학회지
• /
• 제39권6호
• /
• pp.899-912
• /
• 2002

In this paper, the boundedness of some commutators related to linear operators on weak Herz spaces are obtained.

• 충청수학회지
• /
• 제26권3호
• /
• pp.605-613
• /
• 2013

In this paper, we investigate bounds for solutions of perturbed nonlinear differential systems.

• Korean Journal of Mathematics
• /
• 제5권2호
• /
• pp.227-232
• /
• 1997

Banach-Steinhaus type results are established for sequentially continuous operators and bounded operators between locally convex spaces without barrelledness.

• 대한수학회지
• /
• 제45권1호
• /
• pp.229-248
• /
• 2008

The boundedness and compactness of the Volterra composition operators between weighted Bergman spaces and Bloch type spaces are discussed in this paper.

• 충청수학회지
• /
• 제9권1호
• /
• pp.165-174
• /
• 1996

Using the comparison principle and inequalities we obtain some results on boundedness and stabilities of solutions of the nonlinear functional differential equation $y^{\prime}=f(t,y)+g(t,y,Ty)$.

• 충청수학회지
• /
• 제27권2호
• /
• pp.335-345
• /
• 2014

In this paper, we investigate bounds for solutions of nonlinear perturbed functional differential systems.

• 대한수학회논문집
• /
• 제21권3호
• /
• pp.465-474
• /
• 2006

In this paper, we characterize the boundedness and compactness of weighted composition operators ${\psi}C_{\varphi}f={\psi}fo{\psi}$ acting between Bergman-type spaces.