G. Z. Li, “The Fixed Point Index and the Fixed Point Theorems of 1-Set-Contrac-Tive Mappings,” Proceedings of the American Mathematical Society, Vol. 104, No. 4, 1988, pp. 1163-1170. doi:10.1090/S0002-9939-1988-0969052-9

has been cited by the following article:

• TITLE: Operator Equation and Application of Variation Iterative Method

  AUTHORS: Ning Chen, Jiqian Chen

  KEYWORDS: Topology Degrees and Index; 1-Set-Contract Operators; Modified Variation Iteration Method; Integral-Differential Equation

  JOURNAL NAME: Applied Mathematics, Vol.3 No.8, August 1, 2012

  ABSTRACT: In this paper, we study some semi-closed 1-set-contractive operators A and investigate the boundary conditions under which the topological degrees of 1-set contractive fields, deg (I-A, Ω, p) are equal to 1. Correspondingly, we can obtain some new fixed point theorems for 1-set-contractive operators which extend and improve many famous theorems such as the Leray-Schauder theorem, and operator equation, etc. Lemma 2.1 generalizes the famous theorem. The calculation of topological degrees and index are important things, which combine the existence of solution of for integration and differential equation and or approximation by iteration technique. So, we apply the effective modification of He’s variation iteration method to solve some nonlinear and linear equations are proceed to examine some a class of integral-differential equations, to illustrate the effectiveness and convenience of this method.