‎in this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.

Let ∆∞ = End([∞]) be the monoid of convergent monotonic sequences in N∪{∞}. The category Pre(∆∞) of sequential sets is the category whose objects are sets equipped with an action of this monoid, and whose morphisms are equivariant maps. We call a category C sequentially generated if it is a localization of Pre(∆∞). In this paper we show that several important categories, including the category ...

In this paper, we present a Tseng-type self-adaptive algorithm for solving variational inequality and fixed point problem involving pseudomonotone pseudocontractive operators in Hilbert spaces. A weak convergent result such is proved under weaker assumption than sequentially weakly continuous imposed on the operator. Some corollaries are also included.

We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in which convergent sequences have unique limits. We also answer a question of D.E. Cameron by showing that each sequentially compact topology is contained in a ...

We show that if X is a tight subspace of C(K) then X has the Pe lczyński property and X is weakly sequentially complete. We apply this result to the space U of uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove that U has the Pe lczyński property and U is weakly sequentially complete. Using separate methods, we prove U and U have the Dunford...

A globally convergent homotopy method is deened that is capable of sequentially producing large numbers of stationary points of the multi-layer perceptron mean-squared error surface. Using this algorithm large subsets of the stationary points of two test problems are found. It is shown empirically that the MLP neural network appears to have an extreme ratio of saddle points compared to local mi...

A globally convergent homotopy method is defined that is capable of sequentially producing large numbers of stationary points of the multi-layer perceptron mean-squared error surface. Using this algorithm large subsets of the stationary points of two test problems are found. It is shown empirically that the MLP neural network appears to have an extreme ratio of saddle points compared to local m...

Cardinal invariants related to sequential separability of generalized Cantor cubes 2κ, introduced by M. Matveev, are studied here. In particular, it is shown that the following assertions are relatively consistent with ZFC: (1) 2ω1 is sequentially separable, yet there is a countable dense subset of 2ω1 containing no non-trivial convergent subsequence, (2) 2ω1 is not sequentially separable, yet ...