linear map

(redirected from Nonlinear operator)

linear map

(mathematics)
(Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v).
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in periodicals archive ?
We describe a nonlinear operator as [mathematical expression not reproducible] and thus
He added that the theme of the conference will cover the major areas of Mathematical sciences such as; Functional Analysis and its Applications, Fluid Dynamics, Fuzzy logic, Topological Vector Spaces and Nonlinear Operator Theory, Best Approximations Theory, Soft Set Theory, Graph Theory, Algebra and more.
where [phi] is an unknown function in [LAMBDA](= [0, 1] x [0,1]) which should be determined and f(x, t), [[phi].sub.0](x) are known functions and N is a nonlinear operator. The given functions f(x, t) and [phi](x, t) are assumed to be sufficiently smooth in order to guarantee the existence and uniqueness of a solution [phi] [member of] C(A).
where f is a nonlinear operator defined on a convex subset D of a complex dimension space C.
of (18) we introduce the nonlinear operator [N.sub.q]: [Y.sup.0.sub.q] [right arrow] [Y.sup.0.sub.q], as
He, "A Fixed Point Theorem for Systems of Nonlinear Operator Equations and Applications to (p1, p2)-Laplacian System," Mediterranean Journal of Mathematics, vol.
Zhang, "Positive solutions for nonlinear operator equations and several classes of applications," Mathematische Zeitschrift, vol.
The methodology which is adopted to predict the reservoir properties includes the estimation of a nonlinear operator. This nonlinear operator is then used to predict the well logs from the adjacent seismic attributes data (Lindseth, 1979).
The ADM combined with the use of symbolic algebra packages such as MATHEMATICA or MAPLE is a powerful method for solving nonlinear operator equations including ordinary or partial differential equations [14, 36].
Let G : D [subset or equal to] X [right arrow] Y be a nonlinear operator; [k.sub.0], k, [k.sub.1], [k.sub.2], [eta], and s are given parameters.
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

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