• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.53-66
• /
• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.

• Communications of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.447-456
• /
• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.447-459
• /
• 1995

A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.375-388
• /
• 2013

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.505-512
• /
• 2012

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mappings and nonspreading mappings and the set of solution of an equilibrium problem on the setting of real Hilbert spaces.

• East Asian mathematical journal
• /
• v.29 no.3
• /
• pp.303-314
• /
• 2013

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of asymptotically ${\kappa}$-strict pseudo-contractions in Hilbert spaces. Weak and strong convergence theorems are established for the iterative scheme.

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.691-700
• /
• 2004

Let X and Y be operators acting on a Hilbert space and let (equation omitted) be a subspace lattice of orthogonal projections on the space containing 0 and I. We investigate normal interpolation problems in Alg(equation omitted): Given operators X and Y acting on a Hilbert space, when does there exist a normal operator A in Alg(equation omitted) such that AX = Y?

• Communications of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.765-777
• /
• 2016

In this paper, we propose a new modied Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.371-376
• /
• 2002

The aim of this paper is to study the condition of η-concavity. We will give examples of η-functions in Hilbert spaces on two different domains.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.205-235
• /
• 2023

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.