The Solution Of Nonlinear Integral Equation And Isometric Problems In Space

In this paper,the Aleksandrov problem on non-Archimedes 2-fuzzy 2-normed space,that is,the equidistant problem,and the solutions of the bounded difference functions of the two types of nonlinear integral equations(nonlinear Hammerstein integral equation and nonlinear Volterra integral equation)are studied,and corresponding results are obtained.In the first chapter,we review the research on Aleksandrov's problem,and introduce the definition of non Archimedean 2-fuzzy 2-Normed space and the definition form of its norm.By referring to Benz's theorem,we get that the mapping is 2-equidistant when it satisfies AOPP and(1.3.2).In the second chapter,we introduce the contents of two kinds of nonlinear integral equations and the research of their variation solutions,and give the definition of bounded variation normed space and the definition form of its norm.Through Banach contraction theorem and the hypothesis of condition(H1-H9),we get the bounded p-variation local solutions and the continuous bounded p-variation local solutions of the two kinds of nonlinear integral equations,and according to the alternative of Leray Schauder theorem,the global solution of Hammerstein integral equation with bounded p-variation is obtained.In the third chapter,the definition of bounded difference normed space in n-dimensional space and the definition form of norm are introduced.Based on the existing conclusions of two kinds of nonlinear integral equations in[27]and[32],the bounded variation function solution in n-dimensional space is obtained.