Abstract:
Recently Abbas [M. Abbas, Coincidence points of multivalued f−almost nonexpansive mappings, Fixed
Point Theory, 13 (1) (2012), 3–10] introduced the concept of f−almost contraction which generalizes the
class of multivalued almost contraction mapping and obtained coincidence point results for this new class
of mappings. We extend this notion to multivalued f−almost F−contraction mappings and prove the
existence of coincidence points for such mappings. As a consequence, coincidence point results are obtained
for generalized multivalued f−almost F−nonexpansive mappings which assume closed values only. Related
common fixed point theorems are also proved. In the last section, applications of our results in dynamic
programming and integral equations to show the existence and uniqueness of solutions are obtained. We
present some remarks to show that our results provide extension as well as substantial generalizations and
improvements of several well known results in the existing comparable literature.
