Wiyada Kumam

A Shrinking Projection Method for Generalized Mixed Equilibrium Problems, Variational Inclusion Problems and a Finite Family of Quasi-Nonexpansive Mappings

The purpose of this paper is to consider a shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of fixed points of a finite family of quasi-nonexpansive mappings, and the set of solutions of variational inclusion problems. Then, we prove a strong convergence theorem of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend recent results announced by Peng et al. (2008), Takahashi et al. (2008), S.Takahashi and W. Takahashi (2008), and many others.

Generalized Systems of Variational Inequalities and Projection Methods for Inverse-Strongly Monotone Mappings

We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to find solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of the paper we utilize our results to study some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extend and improve the results of Ceng et al., (2008) and many others.

Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces

In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem.

A new Hybrid Projection Algorithm for Solving the Split Generalized Equilibrium Problems and the System of Variational Inequality Problems

In this paper, we introduced modified Mann iterative algorithms by the new hybrid projection method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of the split generalized equilibrium problem and the set of solutions of the general system of the variational inequality problem for two-inverse strongly monotone mappings in real Hilbert spaces. The strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions are provided.

Random fixed points of multivalued random operators with property (D)

The purpose of this paper is to prove some random fixed point theorem for multivalued nonexpansive non-self random operators. We will prove the existence of a random fixed point theorem for multivalued non-self random operator in the framework of a Banach space with property (D), and satisfying an inwardness condition. Our work also extends the stochastic version of the results of Kumam [P. Kumam, A note on some fixed point theorems for set-valued non-self mappings in Banach spaces. Int. Journal of Math. Analysis, to appear.], and improves the work of Kumam and Plubtieng [P. Kumam and S. Plubtieng, Random fixed point theorems for multivalued nonexpansive operators in uniformly nonsquare Banach spaces. Random Oper. and Stoch. Equ. 14(1) (2006), 35–44.].

Solutions of system of equilibrium and variational inequality problems on fixed points of infinite family of nonexpansive mappings

In this paper, we introduce a hybrid viscosity approximation scheme for finding a common element of the solution set for a system of equilibrium problems, the solution set for a system of variational inequality problems and the common fixed point set for an infinite family of nonexpansive mappings in Hilbert spaces. Then we prove the strong convergence of the proposed iterative scheme. Our results improve and extend the results announced by Ceng and Yao (2008) 4.

Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations

Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results.MSC:46S40, 47H10, 34A70, 54E50.

Optimization for estimation to medical service value of informal workers social security office in Thailand

Abstract The objective of this study is to find the model of medication expense of labor that is out of social security system by using data from Social Security Office: Year 2010 Data surveyed from Thai People. The data is classified to be 3 group by the type of labor that is out of social security system receiving the medical service as the patient of hospital as following: outpatient, inpatient without operation and inpatient with operation. As the data that is collected is not stable, Fuzzy Method is applied for analysis to find the model of medical expense of labor that is out of social security system. Therefore, the total medical expense is the sum of these three models.

Convergence analysis of modified Picard-S hybrid iterative algorithms for total asymptotically nonexpansive mappings in Hadamard spaces

ABSTRACT In this paper, we introduce new type iterative scheme called a ‘modified Picard-S hybrid’ iterative algorithm to establish Δ-convergence and strong convergence theorems under suitable conditions for total asymptotically nonexpansive mappings in CAT(0) spaces. Our results in the paper improve and extend many results appeared in the literature. Moreover, we also illustrate numerical examples for the proposed iteration process to compare speed of convergence among the existing iterative algorithms.

A Method for Optimal Solution of Intuitionistic Fuzzy Transportation Problems via Centroid

In this work, we introduce the method for solving intuitionistic fuzzy transportation problem (IFTP) in which supplies and availability are crisp numbers and cost is intuitionistic fuzzy number (IFN). We are using centroid of IFN for the representative value of the intuitionistic fuzzy cost. In addition we are using allocation table method (ATM) to find an initial basic feasible solution (IBFS) for the IFTP. Moreover, this method is also good optimal solution in the literature and illustrated with numerical examples.