A fixed point result for mappings on the l(infinity)-sum of a closed and convex set based on the degree of nondensifiability

摘要

Let C a non-empty, bounded, closed and convex subset of a Banach space X, and denote by l(infinity)(C) the l(infinity)-sum of C. In the present paper, by using the degree of nondensifiability (DND), we introduce the class of r-Delta-DND-contraction maps f : l(infinity)(C) -> X and prove that if f (l(infinity)(C))/ subset of C then there is some x* is an element of C with f(x*, x*, ... , x*; ... ) = x*. Our result, in the specified framework, generalizes other fixed point results for the so called generalized r-contraction and even other existing fixed point result based on the DND. Also, we derive a new Krasnosel'skii-type fixed point result.