• Korean Journal of Mathematics
• /
• v.25 no.1
• /
• pp.99-116
• /
• 2017

The aim of this article is to introduce a new form of Kantorovich $Sz{\acute{a}}sz$-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.463-475
• /
• 2009

This paper deals with the regularity properties for a class of semilinear integrodifferential functional differential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given.

• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.757-769
• /
• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.985-999
• /
• 2018

This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.695-706
• /
• 1996

In the control system $ \dot{x} = f(t,x(t)) + g(t,x(t))\dot{u}, x(0) = \bar{x}, t \in [0,T], $ this paper shows that the map from u with $L^1(m)$-topology to $x_u$ with $L^1(\mu)$-topology is Lipschitz continuous where f is $C^1$, $\mu$ is the Stieltjes measure derived from the function g which is not smooth in the variable t and $x_u$ is the solution of the above system corresponding to u under the assumption that $\dot{u}$ is bounded.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.313-325
• /
• 2010

General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed, and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.

• Journal of applied mathematics & informatics
• /
• v.30 no.1_2
• /
• pp.173-181
• /
• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• The Pure and Applied Mathematics
• /
• v.18 no.3
• /
• pp.219-230
• /
• 2011

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.469-481
• /
• 2020

In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.563-571
• /
• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.