MATHEMATICAL SCIENCES
Year:2013 | Volume:7 | Issue:-|Papers Count:6

There exist many sixth-order iterative methods for solving nonlinear scalar equations. The purpose of this work is to bring them together. We develop a scheme for unifying sixth-order iterative methods. Convergence analysis shows that the methods and family of methods, formulated through the scheme are sixth-order convergent. Finally, some computational results are reported to verify the developed theory.

Purpose: In this paper, a new algorithm is presented for solving one-dimensional parabolic partial differential equations subject to integral conditions.Methods: The algorithm is based on the transverse method of lines and the reproducing kernel method. The transverse method of lines can reduce a one-dimensional parabolic partial differential equation subject to integral conditions to a series of ordinary differential equations (ODEs) with integral boundary conditions. The reproducing kernel method is a relative new analytical technique, which can solve successfully ODEs with integral boundary conditions.Results: The present method combines advantages of these two methods.Conclusions: Numerical results show that the present method is quite efficient.

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using these matrices, the nonlinear two-dimensional Volterra integro-differential equation has been reduced to an algebraic system. Some numerical examples are presented to illustrate the effectiveness and accuracy of the method.

This paper deals with maximal m-open sets. The m-closure and the m-interior of maximal m-open sets and their properties are investigated. Further, the behaviors of maximal m-open sets in m-homeomorphic m-spaces and product m-spaces are inspected. Our results are supported by some examples and counterexamples.

In this paper, the concept of ¶*-quasiconvexity is introduced by using convexifactors. Mond-Weir-type and Schaible-type duals are associated with a multiobjective fractional programming problem, and various duality results are established under the assumptions of ¶*-pseudoconvexity and ¶*-quasiconvexity.

Purpose: In this paper, we introduce and study an iterative method to approximate a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces.Methods: We prove a strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions.Results: We obtain a strong convergence result for approximating a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces, which is a unique solution of a variational inequality problem. Further, we obtain some consequences of our main result.Conclusions: The results presented in this paper are the supplement, extension, and generalization of results in the study of Plubtieng and Punpaeng and that of Cianciaruso et al. The approach of the proof given in this paper is also different.