Ravi P. Agarwal, Donal O'Regan, and Mohamed-Aziz Taoudi

Fixed Point Theory for Multivalued Weakly Convex-Power Condensing Mappings with Application to Integral Inclusions

abstract:
In this paper we present new fixed point theorems for multivalued maps which are convex-power condensing relative to a measure of weak noncompactness and have weakly sequentially closed graph. These results are then used to investigate the existence of weak solutions to a Volterra integral inclusion with lack of weak compactness. In the last section we discuss convex-power condensing multivalued maps with respect to a measure of noncompactness.

Mathematics Subject Classification: 47H10, 47H30

Key words and phrases: Convex-power condensing multivalued maps, fixed point theorems, measure of weak noncompactness, weak solutions, Volterra integral inclusions