A criterion for Cauchy sequences in db-metric spaces
In this note a criterion for Cauchy sequences is proved which refines the one presented in `Cauchy sequences in b-metric spaces', Topology Appl. 373 (2025) 109477.
math.GN↗
arXiv subjects
Lech Pasicki
Publications and source records attributed to Lech Pasicki.
My last fixed point theorem
In this note a far extension of the Banach fixed point theorem is proved.
math.GM↗
Contractions, inwardness, tool theorems
The paper is devoted to the fixed point theory in four aspects: of contractions, nonexpansive mappings, generalized inward mappings, and of the tool theorems. The manuscript was written about ten years ago. At first Nadler's concept of contraction for multivalued mappings is replaced here by a more general, and yet elegant condition: for some $\alpha + \epsilon <1$, and each $x \in X$ there exists a $y \in F(x)$ such that $d(F(y),y) \leq \alpha d(y,x) \leq (\alpha + \epsilon) d(F(x),x)$}. For ``nonexpansive'' mappings we apply bead spaces that are more general than uniformly convex spaces, and our requirements on mappings are weaker than nonexpansivity in the sense of the Hausdorff distance. In the last, third section the Caristi theorem is replaced by more specialized ``tools'', and we apply them to obtain stronger fixed point theorems on generalized inward mappings. In particular, if for each $x \in X$ a nearest point of $F(x)$ belongs to the generalized inward set, then the values of $F$ need not to be closed.
math.GN↗
Istances and Br\o ndsted's variational principle
The manuscript contains elegant extensions of the fundamental variational principles: Br\o ndsted's and Ekeland's. On the other hand we get general and precise version of the Takahashi and the Cariste fixed point theorems. The results are based on the notion of istance for uniform spaces.
math.FA↗
Nonexpansive fixed point theorems for primitive uniform spaces
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
math.GN↗
A Stokes theorem for everyone
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty general, as we assume the differential form to be continuous on a compact set F(A) and C1 "inside" while F(A) is built of "bricks" and its inner part is a C1 manifold. There is no problem of orientability and the integrals under consideration are convergent. The proof is based on integration by parts and inner approximation.
math.CA↗