Implicit and explicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings.
Implicit variational-like inclusions involving general -monotone operators.
In a Nonreflexive Space the Subdifferential is Not Onto.
Inertial forward-backward splitting method in Banach spaces with application to compressed sensing
We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces.
Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities
We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...
Interpolation theorem for the p-harmonic transform
We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation . In this example the p-harmonic transform is essentially inverse to . To every vector field our operator assigns the gradient of the solution, . The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...
Iterative algorithm for approximating solutions of maximal monotone operators in Hilbert spaces.
Iterative approaches to find zeros of maximal monotone operators by hybrid approximate proximal point methods.
Iterative convergence of resolvents of maximal monotone operators perturbed by the duality map in Banach space.
Iterative schemes for fixed points of relatively nonexpansive mappings and their applications.
Iterative schemes for zero points of maximal monotone operators and fixed points of nonexpansive mappings and their applications.
Iterative solution of unstable variational inequalities on approximately given sets.
Iterative solutions of -positive definite operator equations in real uniformly smooth Banach spaces.