• Journal of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.803-829
• /
• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• Journal of the Korean Society of Industry Convergence
• /
• v.8 no.3
• /
• pp.143-148
• /
• 2005

This paper presents a hybrid method for recognizing the faces by using principal component analysis(PCA) and fixed-point independent component analysis(FP-ICA). PCA is used to whiten the data, which reduces the effects of second-order statistics to the nonlinearities. FP-ICA is applied to extract the statistically independent features of face image. The proposed method has been applied to the problems for recognizing the 20 face images(10 persons * 2 scenes) of 324*243 pixels from Yale face database. The 3 distances such as city-block, Euclidean, negative angle are used as measures when match the probe images to the nearest gallery images. The experimental results show that the proposed method has a superior recognition performances(speed, rate). The negative angle has been relatively achieved more an accurate similarity than city-block or Euclidean.

• Nuclear Engineering and Technology
• /
• v.49 no.5
• /
• pp.1095-1099
• /
• 2017

A fission source can act as a stabilization element in coupled Monte Carlo simulations. We have observed this while studying numerical instabilities in nonlinear steady-state simulations performed by a Monte Carlo criticality solver that is coupled to a xenon feedback solver via fixed-point iteration. While fixed-point iteration is known to be numerically unstable for some problems, resulting in large spatial oscillations of the neutron flux distribution, we show that it is possible to stabilize it by reducing the number of Monte Carlo criticality cycles simulated within each iteration step. While global convergence is ensured, development of any possible numerical instability is prevented by not allowing the fission source to converge fully within a single iteration step, which is achieved by setting a small number of criticality cycles per iteration step. Moreover, under these conditions, the fission source may converge even faster than in criticality calculations with no feedback, as we demonstrate in our numerical test simulations.

• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.1-24
• /
• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• Communications of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.421-436
• /
• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.225-258
• /
• 2024

In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.

• Journal of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.247-255
• /
• 1997

In this paper, we are concerned with the existence of positive solutions for the boundary value problems of the form; $$(1) u"(t) + q(t)g(u(t)) = 0, 0 < t < 1 $$ $$ u(0) = 0 = u(1), $$ where q is singular at 0 and /or 1.or 1.

• East Asian mathematical journal
• /
• v.36 no.5
• /
• pp.571-581
• /
• 2020

In this paper, an equilibrium problems involving a finite family of maximal monotone operators and inverse-strongly monotone operators are introduced and investigated. A strong convergence theorem of common solutions is obtained in Hilbert spaces.

• East Asian mathematical journal
• /
• v.32 no.5
• /
• pp.621-633
• /
• 2016

We establish the existence of positive solutions to nonlocal boundary value problems with integral boundary condition and non-negative real boundary parameter by mainly using the Schauder-Fixed point theorem.

• The Pure and Applied Mathematics
• /
• v.28 no.1
• /
• pp.15-26
• /
• 2021

The purpose of this paper is to introduce a new type of a cubic functional equation and then investigate its stability problems in a convex modular space with a generalized ∆a-condition.