In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination number. We define the k-tuple domatic number of G as the largest number of sets in a partition of V into k-tuple dominating sets. Recall that when k = 1, a k-tuple domatic number is the well-studied domatic number. In this work, we derive basic properties and bounds for the k-tuple domatic number.

In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative examples are provided to demonstrate the applicability and simplicity of our scheme.

n this paper, we prove some common fixed point theorems for multivalued mappings and we present some new generalization contractive conditions under the condition of weak compatibility. Our results extends Chang-Chen’s results as well as ´Ciri´c results. An example is given to support the usability of our results.

There are two interesting methods, in the literature, for solving fuzzy linear programming problems in which the elements of coefficient matrix of the constraints are represented by real numbers and rest of the parameters are represented by symmetric trapezoidal fuzzy numbers. The first method, named as fuzzy primal simplex method, assumes an initial primal basic feasible solution is at hand. The second method, named as fuzzy dual simplex method, assumes an initial dual basic feasible solution is at hand. In this paper, the shortcomings of these methods are pointed out and to overcome these shortcomings, a new method is proposed to determine the fuzzy optimal solution of such fuzzy problems. The advantages of the proposed method over existing methods are discussed. To illustrate the proposed method a numerical example is solved by using the proposed method and the obtained results are discussed.

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.

In this paper, we study a class of boundary value problem involving the p-Laplacian oprator and singular nonlinearities. We analyze the existence a critical parameter $lambda^{ast}$ such that the problem has least one solution for $lambdain(0,lambda^{ast})$ and no solution for $lambda>lambda^{ast}.$ We find lower bounds of critical parameter $lambda^{ast}$. We use the method of sub-supersolution to establish our results.

Abstract. The Sturm-Liouville boundary value problem of the multi-order fractional differential equation is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.