Displaying 1241 – 1260 of 1323

Showing per page

Truncated spectral regularization for an ill-posed non-linear parabolic problem

Ajoy Jana, M. Thamban Nair (2019)

Czechoslovak Mathematical Journal

It is known that the nonlinear nonhomogeneous backward Cauchy problem u t ( t ) + A u ( t ) = f ( t , u ( t ) ) , 0 t < τ with u ( τ ) = φ , where A is a densely defined positive self-adjoint unbounded operator on a Hilbert space, is ill-posed in the sense that small perturbations in the final value can lead to large deviations in the solution. We show, under suitable conditions on φ and f , that a solution of the above problem satisfies an integral equation involving the spectral representation of A , which is also ill-posed. Spectral truncation is used...

Two generic results in fixed point theory

Simeon Reich, Alexander J. Zaslavski (2007)

Banach Center Publications

We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finite-dimensional Euclidean spaces.

Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes

Biagio Ricceri (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we first establish a result on the structure of the set of fixed points of a multi-valued contraction with convex values. As a consequence of this result, we then obtain the following theorem: Let ( U , U ) , ( V , V ) be two real Banach spaces and let Φ be a continuous linear operator from U onto V . Put: α = sup { inf { u U : u Φ - 1 ( v ) } : v V , v V 1 } . Then, for every v V and every lipschitzian operator Ψ : U V , with Lipschitz constant L such that α L < 1 , the set { u U : Φ ( u ) + Ψ ( u ) = v } is non-empty and arc wise connected.

Currently displaying 1241 – 1260 of 1323