• East Asian mathematical journal
• /
• v.34 no.1
• /
• pp.47-58
• /
• 2018

In this paper, we consider a fuzzy nonlinear random variational inclusion problems involving ordered RME-multivalued mapping in ordered Banach spaces. By using the random relaxed resolvent operator and its properties, we suggest an random iterative algorithm. Finally both the existence of the random solution of the original problem and the convergence of the random iterative sequences generated by random algorithm are proved.

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.565-575
• /
• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• Communications of the Korean Mathematical Society
• /
• v.18 no.3
• /
• pp.459-468
• /
• 2003

In this paper, we introduce and study a new class of the generalized set-valued mixed variational inequalities. Using the resolvent operator technique, we construct a new iterative algorithm for solving this class of the generalized set-valued mixed variational inequalities. We prove the existence of solutions for the generalized set-valued mixed variational inequalities and the convergence of the iterative sequences generated by the algorithm.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.693-702
• /
• 2009

In this paper, we introduce and study a system of mixed variational inequalities in Banach spaces. By using J-proximal mapping and its Lipschitz continuity for a nonconvex, lower semicontinuous, subdifferentiable, proper functional, an iterative algorithm for computing the approximate solutions of system of mixed variational inequalities is suggested and analyzed. The convergence criteria of the iterative sequences generated by iterative algorithm is also discussed.

• East Asian mathematical journal
• /
• v.27 no.5
• /
• pp.585-595
• /
• 2011

In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational- like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

• Kyungpook Mathematical Journal
• /
• v.53 no.3
• /
• pp.479-495
• /
• 2013

Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $n$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.

• Journal of KIISE:Software and Applications
• /
• v.32 no.8
• /
• pp.795-807
• /
• 2005

The classical approaches for computing Live Variable Analysis(LVA) use iterative algorithms across the entire programs based on the Data Flow Analysis framework. In case of Zephyr compiler, average execution time of LVA takes $7\%$ of the compilation time for the benchmark programs. The classical LVA algorithm has many aspects for improvement. The iterative algorithm for LVA scans useless basic blocks and calculates large sets of variables repeatedly. We propose the improvement of Iterative algorithm for LVA based on used variables' upward movement. Our algorithm produces the same result as the previous iterative algorithm. It is based on use-def chain. Reordering of applying the flow equation in DFA reduces the number of visiting basic blocks and redundant flow equation executions, which improves overall processing time. Experimental results say that our algorithm ran reduce $36.4\%\;of\;LVA\;execution\;time\;and\;2.6\%$ of overall computation time in Zephyr compiler with benchmark programs.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.37-48
• /
• 2009

In the theory and the applications of Numerical Linear Algebra, the class of H-matrices is very important. In recent years, many appeared works have proposed iterative criterion for H-matrices. In this paper, we provide a new type of interleaved iterative algorithm, which is always convergent in finite steps for H-matrices and needs fewer iterations than those proposed in the related works, and a corresponding algorithm for general matrix, which eliminates the redundant computations when the given matrix is not an H-matrix. Finally, several numerical examples are presented to show the effectiveness of the proposed algorithms.

• Proceedings of the KIEE Conference
• /
• 2003.07a
• /
• pp.125-127
• /
• 2003

The Conventional time-domain simulation of transient stability requires iterative calculation procedures to consider the saliency of generator. Recently, a non-iterative algorithm has successfully developed to take into account the generator saliency exactly with the use of $E_q'$-model. This study proposes an extended non-iterative algorithm by adopting the two-axis generator model. Given internal voltages and rotor angles of the generators, network voltages and generator currents can be directly calculated by solving a linear algebraic equation, which enables us to reduce the computation time remarkably.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.749-780
• /
• 2021

In this paper, we give the notion of M(., .)-𝜂-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of M(., .)-𝜂-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.