In the present paper, considering a recent technique, which is used by Wardowski  for fixed points of single-valued mappings, we give a new and general class of multivalued weakly Picard operators on complete metric spaces and show that the class of multivalued almost contractions (both linear and nonlinear cases in the sense of Berinde and Berinde ) is a proper subset of this new class. We also give a nontrivial example showing this fact.
"Recent developments about multivalued weakly Picard operators." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 411 - 422, august 2015. https://doi.org/10.36045/bbms/1442364588