Approximation of fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces.
We obtain modular convergence theorems in modular spaces for nets of operators of the form , w > 0, s ∈ G, where G and H are topological groups and is a family of homeomorphisms Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.
We address some questions concerning a class of differential variational inequalities with finite delays. The existence of exponential decay solutions and a global attractor for the associated multivalued semiflow is proved.
Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy -contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense,...
This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.