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In this paper, we provide a constructive method for hierarchical trajectory refinement.
Among these fixed point theorems only a few have practical importance, i.e., they provide a constructive method for finding fixed point(s).
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In particular, the Banach contraction principle provides a constructive method of finding a unique solution for models involving various types of differential and integral equations.
The Banach contraction mapping principle is the most important in mathematics analysis, it guarantees the existence and uniqueness of a fixed point for certain self-mapping in metric spaces and provides a constructive method to find this fixed point.
It guarantees the existence and uniqueness of fixed points for certain self-maps in a complete metric space and provides a constructive method to find those fixed points.
All the above observations motivate for constructive study of coupled fixed points of a bivariate mapping F : X × X → X satisfying a weaker contractive condition of nonexpansiveness type and providing a constructive method to approximate these coupled fixed points, which we generally meet in applications, i.e., when we have equality of the coupled fixed point components.
It is well known [21, 27] that Banach's theorem also provides a constructive method to calculate the fixed point by successive iterations.
A constructive method for the construction of an optimal input signal for achieving guaranteed detection with specified precision is presented.
In this paper a system theoretic approach is employed to derive a constructive method for the control design.
Among these (common) fixed point theorems, only a few give a constructive method for finding the fixed points or the common fixed points of the mappings involved.
He proved this by giving a constructive method for finding all of the invariants and their generators, but was not able to carry out this constructive approach for invariants in three or more variables.
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