Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits.
The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for ---contraction in a complete metric space. We extend the concept of -contraction into an ---contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.
We show that many generalisations of Borsuk-Ulam's theorem follow from an elementary result of homological algebra.
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.