Sentence examples for mapping is assumed from inspiring English sources

Since a best proximity point reduces to a fixed point if the underlying mapping is assumed to be self-mappings, the best proximity point theorems are natural generalizations of the Banach contraction principle.

One finds that best proximity point theorems are natural generalizations of the contraction principle to the case of non-self-mappings because a best proximity point reduces to a fixed point if the underlying mapping is assumed to be self-mapping.

It is clear that a fixed point coincides with a best proximity point if d ( A, B ) = 0. Since a best proximity point reduces to a fixed point if the underlying mapping is assumed to be self-mappings, the best proximity point theorems are natural generalizations of the Banach's contraction principle.

The set-valued mapping is assumed to be upper semi-continuous compact with nonempty closed convex values.

The main objective of this paper is to further extend and establish some new Ulam type stability results of the quadratic functional equations mentioned above, in which the quadratic mapping is assumed to be a fuzzy set-valued mapping.

The above mentioned mapping is assumed to be defined from one set A to the other set B. Then under suitable conditions, by applying fixed point methodologies, we obtained a best proximity point of the above mentioned mapping which realizes the minimum distance.

They also presented a sufficient condition to ensure the existence of a solution to the generalized variational inequality, and the set-valued mapping was assumed to be upper semi-continuous with nonempty compact convex values.

So, if a flexible genetic architecture and non-linear mapping are assumed, not the phenotypic differentiation, but the genotypic differences underlying this differentiation are constrained under sexual reproduction.

This notion has been confirmed by models of sympatric speciation in which a fixed genetic architecture and a linear genotype phenotype mapping were assumed.

The depth map is assumed to be constant in the neighborhood of the filtering pixel x0, where neighborhood is found by the LPA-ICI procedure.

In consecutive static frames or areas with low motion, the depth map is assumed to be the same for that sequence of frames.