http://www.iaumath.com The latest research articles published by Mathematical Sciences 2013-05-14T00:00:00Z For a given connected graph G=(V,E), a set Dtr¿V (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 ¿tr(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) ¿tr(G)=n, (2) ¿(G)=1 and ¿tr(G)=3, and (3) ¿tr(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 ¿-set of cardinality 2. http://www.iaumath.com/content/7/1/26 Zahra Tahmasbzadehbaee D Soner Nandappa Hossein Abdollahzadeh Ahangar Doost Ali Mojdeh Yancai Zhao Mathematical Sciences 2013, null:26 2013-05-14T00:00:00Z doi:10.1186/2251-7456-7-26 /content/figures/2251-7456-7-26-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 26 2013-05-14T00:00:00Z PDF In this article, a Petrov-Galerkin method, in which the element shape functions are cubic and weightfunctions 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 ofthe Maxwellian initial condition into solitary waves are studied using the proposed method. Accuracyand efficiency of the method are demonstrated by computing the numerical conserved laws and L2,L8 error norms. The computed results show that the present scheme is a successful numerical tech-nique for solving the MRLW equation. A linear stability analysis based on the Fourier method is alsoinvestigated. http://www.iaumath.com/content/7/1/25 Seydi Battal Gazi Karakoc Turabi Geyikli Mathematical Sciences 2013, null:25 2013-05-14T00:00:00Z doi:10.1186/2251-7456-7-25 /content/figures/2251-7456-7-25-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 25 2013-05-14T00:00:00Z PDF 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. http://www.iaumath.com/content/7/1/24 Sumit Chandok Wutiphol Sintunavarat Poom Kumam Mathematical Sciences 2013, null:24 2013-05-10T00:00:00Z doi:10.1186/2251-7456-7-24 /content/figures/2251-7456-7-24-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 24 2013-05-10T00:00:00Z PDF Let R be an associative ring with identityand let k ¿ 1 be a fixed integer.An element (x, y) ¿ R × Ris said to be left (right)k-Engel ¿-regular if there exists a positive integer nand an element z ¿ R such that [x, y]nk = z[x, y]kn+1([x, y]nk = [x, y]kn+1z).If every element of R × R is left (right) k-Engel ¿-regular,then R is said to be left (right) k-Engel ¿-regular.An element (x, y) ¿ R × R is strongly k-Engel ¿-regularif it is both left and right k-Engel ¿-regular. The ring R is strongly k-Engel¿-regular if every element of R × R is strongly k-Engel ¿-regular.In this paper, we investigate properties of abelianstrongly k-Engel ¿-regular ring. http://www.iaumath.com/content/7/1/23 Angelina Chin Shervin Sahebi Mathematical Sciences 2013, null:23 2013-05-08T00:00:00Z doi:10.1186/2251-7456-7-23 /content/figures/2251-7456-7-23-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 23 2013-05-08T00:00:00Z PDF 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 (a ,m)-convex. http://www.iaumath.com/content/7/1/22 ¿mdat ¿¿can Mathematical Sciences 2013, null:22 2013-05-06T00:00:00Z doi:10.1186/2251-7456-7-22 /content/figures/2251-7456-7-22-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 22 2013-05-06T00:00:00Z PDF In this paper, we give a generalization of the Baskakov-type operatorsintroduced by Baskakov (Doklady Akademii Nauk SSSR 113:249--251, 1957 (inRussian)) and obtain some direct and inverse results for these newoperators. http://www.iaumath.com/content/7/1/21 Çi¿dem Atakut Sevilay Kirci Serenbay ¿brahim Büyükyazici Mathematical Sciences 2013, null:21 2013-05-04T00:00:00Z doi:10.1186/2251-7456-7-21 /content/figures/2251-7456-7-21-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 21 2013-05-04T00:00:00Z PDF 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. http://www.iaumath.com/content/7/1/20 Hemant Nashine Hassen Aydi Mathematical Sciences 2013, null:20 2013-05-04T00:00:00Z doi:10.1186/2251-7456-7-20 /content/figures/2251-7456-7-20-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 20 2013-05-04T00:00:00Z PDF 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. http://www.iaumath.com/content/7/1/19 Kaleem Kazmi Mohammad Farid Mathematical Sciences 2013, null:19 2013-05-03T00:00:00Z doi:10.1186/2251-7456-7-19 /content/figures/2251-7456-7-19-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 19 2013-05-03T00:00:00Z PDF The aim of this paper is to present some common fixed point resultsfor six selfmappings satisfying generalized weakly(¿, ¿)-contractive condition in the setup of partiallyordered G-metric spaces. Our results extend and generalize thecomparable results in the work of Abbas from the context of ordered metric spaces to the setup of orderedG-metric spaces.Also, our results are supported by an example. http://www.iaumath.com/content/7/1/18 Vahid Parvaneh Abdolrahman Razani Jamal Rezaei Roshan Mathematical Sciences 2013, null:18 2013-04-08T00:00:00Z doi:10.1186/2251-7456-7-18 /content/figures/2251-7456-7-18-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 18 2013-04-08T00:00:00Z PDF In this paper, we prove some common fixed point theorems for weaklycompatible mappings in metric spaces satisfying generalized(¿, ¿)-contractive conditions under the common limitrange property. We present a fixed point theorem for fourfinite families of self-mappings which can be utilized to derivecommon fixed point theorems involving any number offinite mappings. Our results improve and extend the corresponding results ofRadenovi¿ et al. (Bull. Iranian Math. Soc. 38(3):625--645, 2012).We also furnish some illustrative examples to supportour main results. http://www.iaumath.com/content/7/1/16 Mohammad Imdad Sunny Chauhan Zoran Kadelburg Mathematical Sciences 2013, null:16 2013-04-04T00:00:00Z doi:10.1186/2251-7456-7-16 /content/figures/2251-7456-7-16-toc.gif Mathematical Sciences 2251-7456 ${item.volume} 16 2013-04-04T00:00:00Z PDF