MATHEMATICAL SCIENCES
Year:2013 | Volume:7 | Issue:-|Papers Count:12

In this paper, we introduce two iterative schemes for finding a common solution of a generalized vector equilibrium problem and relatively nonexpansive mappings in a real Banach space. We study the strong and weak convergence of the sequences generated by the proposed iterative schemes. The results presented in this paper are the supplement, extension, and generalization of the previously known results in this area.

In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weight functions are quadratic B-splines, is introduced to solve the modified regularized long wave (MRLW) equation. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracy and efficiency of the method are demonstrated by computing the numerical conserved laws and L2, L ¥ error norms. The computed results show that the present scheme is a successful numerical technique for solving the MRLW equation. A linear stability analysis based on the Fourier method is also investigated.

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In this paper, we establish a coupled fixed point result of F: X´X ®X having the mixed monotone property involving generalized altering distance functions in five variables on ordered metric spaces. An example is given to support the usability of our results. We also give a coupled fixed point result involving a contraction of integral type.

We introduce a new iterative algorithm based on a viscosity approximation method for finding the common solution of variational inequality problems for an inverse strongly accretive operator and the solution of fixed point problems for Lipschitzian semigroup mappings in Banach spaces. In controlling suitable conditions, strong convergence theorems are proven. Our results extend and improve the recent results of some authors in the literature in this field.

Let R be an associative ring with identity and let k ³1 be a fixed integer. An element (x,y)ÎR´R is said to be left (right) k-Engel p-regular if there exists a positive integer n and an element z ∈ R such that [ x, y]nk =z[ x, y]n+1 k ([ x, y]nk =[ x, y]n+1 k z). If every element of R´R is left (right) k-Engel p-regular, then R is said to be left (right) k-Engel p-regular. An element (x, y) ∈ R´R is strongly k-Engel p-regular if it is both left and right k-Engel π-regular. The ring R is strongly k-Engel π-regular if every element of R × R is strongly k-Engel p-regular. In this paper, we investigate properties of abelian strongly k-Engel p-regular ring.

In this paper, we give a generalization of the Baskakov-type operators introduced by Baskakov (Doklady Akademii Nauk SSSR 113:249–251, 1957 (in Russian)) and obtain some direct and inverse results for these new operators.

For a given connected graph G = (V, E), a set Dtr ÍV(G) is a total restrained dominating set if it is a dominating set and both (Dtr) and (V(G)- Dtr) do not contain isolated vertices. The cardinality of the minimum total restrained dominating set in G is the total restrained domination number and is denoted by γtr(G). In this paper, we continue the study of total restrained domination number of graphs. We first give some results on total restrained domination number of graphs. And then, we characterize all graphs G of order n for which (1) γtr(G)=n, (2) γ (G)=1 and γtr(G)=3, and (3) γtr(G)=2. Furthermore, we give some bounds on total restrained domination number of graphs with diameter 3. Finally, we present some bounds for total restrained domination number of some planar graphs with diameter 2 and g-set of cardinality 2.

Sintunavarat and Kumam introduced the notion of hybrid generalized multi-valued contraction mapping and established a common fixed point theorem. We extend their result for four mappings and prove common coincidence and common fixed point theorem.

In this paper, numerical solution of nonlinear Hammerstein integral equations via collocation method based on double exponential transformation is considered. Some remarks with respect to the computational cost and stability and implementation are discussed. Examples are presented to illustrate effectiveness of method.

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed g-monotone property in partially ordered G-metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature. To illustrate our results, we give some examples.

 In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are (α,m)-convex.