MATHEMATICAL SCIENCES
Year:2013 | Volume:7 | Issue:-|Papers Count:10

In this article, we are to find the root of a square matrix A. Specially, if matrix A has multiple eigenvalues, we present a manual solution so as to find the root of it. In other words, we focus on solving the equation X2=A and find the solutions.

In this paper, we obtain some fixed point results on subgraphs of directed graphs. We show that the Caristi fixed point theorem and a version of Knaster-Tarski fixed point theorem are special cases of our results.

Using free simplicial algebras with given CW−basis, it is shown how to construct a free or totally free quasi 3-crossed module on suitable construction data. Quasi 3-crossed complexes are introduced and similar freeness results are given for these are discussed.

This paper deals with the solutions of boundary value problems based on the converting differential equation with boundary conditions to a mixed Voletrra and Fredholm integral equation, then, we will use the special case of successive approximations method for solving obtained equation. Convergence analysis and error estimate is discussed, also, a numerical example is presented to demonstrate the accuracy of the proposed technique.

In this paper, we introduce generalized c2 sequence spaces over p-metric spaces defined by Musielak function=(fmn) and study some topological properties.

In this paper, for conformal mapping f, we study the membership of log f 'to the QK (p, q) -type spaces of analytic functions. Moreover, geometric conditions and some important characterizations involving the Schwarzian derivative are also given.

Purpose: The purpose of this paper is to introduce and study the Baskakov- Durrmeyer- Stancu operators based on q-integers.Methods: First we use property of q-calculus to estimate moments of these operators. Also study some approximation properties, asymptotic formula including q-derivative and point-wise estimation for the operators L(a,b)n,q .Results: We studied better error estimations for these operators using King type approach.Conclusions: The results proposed here are new and have a better rate of convergence.

Our purpose is to show the order of approximation and simultaneous approximation, Voronovskaja-type results with quantitative estimate, the exact degree of approximation for complex Szasz-Schurer operators and complex Kantorovich type generalization of Szasz-Schurer operator attached to analytic functions on compact disks.

In this paper, we propose a split nonconvex variational inequality problem which is a natural extension of split convex variational inequality problem in two different Hilbert spaces. Relying on the prox-regularity notion, we introduce and establish the convergence of an iterative method for the new split nonconvex variational inequality problem. Further, we also establish the convergence of an iterative method for the split convex variational inequality problem. The results presented in this paper are new and different form the previously known results for nonconvex (convex) variational inequality problems. These results also generalize, unify, and improve the previously known results of this area.

In this paper, we study the geometry of Lie groups with bi-invariant Finsler metrics. We first show that every compact Lie group admits a bi-invariant Finsler metric. Then, we prove that every compact connected Lie group is a symmetric Finsler space with respect to the bi-invariant absolute homogeneous Finsler metric. Finally, we show that if G is a Lie group endowed with a bi-invariant Finsler metric, then, there exists a bi-invariant Riemanninan metric on G such that its Levi-Civita connection coincides the connection of F.