• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1145-1156
• /
• 2009

In this paper, we consider the existence, uniqueness of the solutions and controllability for the neutral functional integro-differential equations with delay terms by Sadovskii's fixed point theorem.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.501-503
• /
• 1997

The existence of a unique local generalized solution for the abstract functional evolution problem of the type $$ (FDE:\phi) x'(t) + A(t, x_t)x(t) \ni G(t, x_t), t \in [0, T], x_0 = \phi $$ in a general Banach spaces is considered. It is shown that $(FDE:\phi)$ could be considered with well-known fixed point theory and recent results for the functional differential equations involving the operator A(t).

• Communications of the Korean Mathematical Society
• /
• v.28 no.3
• /
• pp.517-526
• /
• 2013

We give a fixed point theorem for complete fuzzy metric space which generalizes fuzzy Banach contraction theorems established by V. Gregori and A. Spena [Fuzzy Sets and Systems 125 (2002), 245-252] using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9] in metric spaces.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.85-98
• /
• 2009

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].

• East Asian mathematical journal
• /
• v.28 no.3
• /
• pp.305-320
• /
• 2012

The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.440-444
• /
• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• Kyungpook Mathematical Journal
• /
• v.58 no.4
• /
• pp.651-675
• /
• 2018

We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.3
• /
• pp.221-234
• /
• 2021

We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.1091-1104
• /
• 2021

In this paper, we prove some coincidence point theorems for mappings satisfying nonlinear Prešić-Ćirić type contraction in complete metric spaces as well as in ordered metric spaces. As a consequence, we deduce corresponding fixed point theorems. Further, we give some examples to substantiate the utility of our results.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.1
• /
• pp.39-52
• /
• 2022

We introduce Clifford-valued neural networks with leakage delays. Furthermore, we study the uniqueness and existence of Clifford-valued Hopfield artificial neural networks having the Stepanov weighted pseudo almost periodic forcing terms on leakage delay terms. However the noncommutativity of the Clifford numbers' multiplication made our investigation diffcult, so our results are obtained by decomposing Clifford-valued neural networks into real-valued neural networks. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.