• Korean Journal of Mathematics
• /
• 제24권2호
• /
• pp.181-198
• /
• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Nonlinear Functional Analysis and Applications
• /
• 제27권2호
• /
• pp.223-232
• /
• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• 호남수학학술지
• /
• 제42권1호
• /
• pp.17-35
• /
• 2020

In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the fixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.

• East Asian mathematical journal
• /
• 제32권5호
• /
• pp.685-700
• /
• 2016

The main object of this work to introduced and studied a new class of fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces. By using the random B-restricted accretive mapping with measurable mappings ${\alpha},{\alpha}^{\prime}:{\Omega}{\rightarrow}(0,1)$, an existence of random solutions for this class of fuzzy general nonlinear ordered random variational inequality (equation) with fuzzy mappings is established, a random approximation algorithm is suggested for fuzzy mappings, and the relation between the first value $x_0(t)$ and the random solutions of fuzzy general nonlinear ordered random variational inequality is discussed.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.381-394
• /
• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

• 전산구조공학
• /
• 제4권2호
• /
• pp.87-94
• /
• 1991

본고에서는 Sandhu등에 의해 개발된 다변수경계치문제의 변분모델화 방법을 이용하여 범함수의 독립변수로써 변위와 응력을 동시에 포함하는 이방성탄성문제의 혼합형변분원리(Mixed Variational Principle)를 유도한다. 탄성방정식을 내적공간에서 self-adjoint한 미분연산자매트릭스 방정식으로 표시한 후 다변수 경계치문제의 변분이론을 적용하므로써 일반적 범함수가 구해지며, 이때에 지배방정식의 미분연산자와 경계조건식의 연산자의 일관성 (Consistency)을 유지하므로써 경계조건도 체계적으로 범함수내에 포함시킬 수 있다. 이 일반적 범함수에서 미분연산자의 self-adjointness성질을 이용하여 응력함수의 도함수를 제거하고 탄성방정식중 특정식이 항상, 정확히 만족된다고 가정하므로써 원하는 혼합형변분원리의 범함수를 유도할 수 있다. 여기에서 유도된 변분원리는 최근 Reissner에 의해 개발된 변분원리와 유사한 물리적 의미를 가지나 유도방법이 다를 뿐 아니라 일반적 이방성탄성체에 적용할 때 보다 편리한 형태로 된다. 이 혼합형변분원리는 다양하게 응용될 수 있으나, 복합재료적층판과 같은 이질성, 이방성 평판이론, 또는 쉘이론의 유도에 유용하게 사용할 수 있다.

• Korean Journal of Mathematics
• /
• 제8권1호
• /
• pp.97-102
• /
• 2000

In this paper, we study the first and second formulas of energy functions on the Teichm$\ddot{u}$ller spaces and prove the relation between index and nullity of Jacobi operator.

• 한국추진공학회지
• /
• 제7권2호
• /
• pp.36-43
• /
• 2003

탄소섬유 T700/Epoxy로 만든 직교이방성 구조로 된 두께가 얇은 압력용기의 반경방향의 변위에 관한 해를 곡선좌표계의 평형방정식을 사용하여 구하였다. 3차원 곡선좌표계의 변형율과 변위의 관계를 간단히 하면서 지배방정식을 유도하기 위해 변분이론과 가상일의 원리를 사용하였다. 다른 여러 종류의 직교이방성 압력용기에 대한 계산 결과를 제시했으며 수압시험을 한 결과와 비교 검토하였다. 계산결과와 시험결과는 비교적 잘 일치하였다.

• 대한수학회보
• /
• 제48권5호
• /
• pp.939-949
• /
• 2011

In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when X and Y are convex sets in topological vector spaces, a new subclass of KKM(X, Y) different by any admissible class $\mathfrak{u}_c$(X, Y). For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.

• Journal of applied mathematics & informatics
• /
• 제19권1_2호
• /
• pp.19-32
• /
• 2005

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.