Sentence examples for mapping principle on from inspiring English sources

We prove this result by the contraction mapping principle on the Banach space.

Without the conditions of the uniform boundedness of the nonlinear terms and the compactness of the principal operators, we obtain the wellposedness and the norm estimate of the given equation by converting the problem into the contraction mapping principle on state space.

Now, we apply the Contraction Mapping Principle on a ball with ratio in the space,, where.

In 1965, Prešić [36] extended the Banach contraction mapping principle to mappings defined on product spaces and proved the following theorem.

In 1965, Prešić [4, 5] extended the Banach contraction mapping principle to mappings defined on product spaces and proved the following theorem.

Moreover, in [15] the maximal L p - L q regularity in a domain is derived automatically with the help of the Weis' operator valued Fourier multiplier theorem, so that a local in time unique existence theorem is proved by using the usual contraction mapping principle based on the maximal L p - L q regularity.

We deal with the well-posedness for solutions of nonlinear integrodifferential equations of second-order in Hilbert spaces by converting the problem into the contraction mapping principle with more general conditions on the principal operators and the nonlinear terms and obtain a variation of constant formula of solutions of the given nonlinear equations.

Firstly, we prove an existence and uniqueness theorem based on the contraction mapping principle in Banach space [26, 28].

The proofs of Theorems 1.2, 1.3 are based on the Banach contraction mapping principle [6].

A contracting mapping theorem on one such space, similar to the classical contracting mapping principle, has been obtained, relying upon the gH-difference.

Of course, the Banach contraction mapping principle [1] is the first important result on fixed points for contractive-type mappings.