such a unified theory could have remarkable consequences even in other fields of mathematics, Including controllability methods in transport theory, A solution of the boundary rigidity problem in geometry, Or a general pseudo-linearization approach for solving

nonlinear operator equations.

This

nonlinear operator is then used to predict the well logs from the adjacent seismic attributes data (Lindseth, 1979).

Many inverse problems can be formulated as a

nonlinear operator equation

The

nonlinear operator eigenvalue problem we are concerned with consists of finding a value [lambda] [member of] B([mu], r) := {[lambda] [member of] C : [absolute value of [lambda] - [mu]] < r} close to [mu][member of] C and a nonzero function f such that

where N is a

nonlinear operator, x denotes the independent variable, and w(x) is an unknown function.

Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the

nonlinear operator stemming from the negative p-Laplacian, i.

This

nonlinear operator is defined on any 8 bit gray scale 256 x 256 pixel image g (x, y).

Here N(g) is a

nonlinear operator from a Hilbert space H into H.

The technique used is based on the decomposition of a solution of

nonlinear operator equation in a series of functions.

1][a,b] and hence the

nonlinear operator A defined by (1.

Zhou, Iterative Methods for

Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, New York, 2002.

where A, with the appropriate boundary condition (Dirichlet, Neumann, periodic), is a suitable linear, unbounded, self-adjoint and positive operator on a suitable Hilbert space H with dense domain D(A) [subset] H, while F is

nonlinear operator and the nonlinear term F(u) can be approximated by Taylor's series (detail is later).