Mann type implicit iteration approximation for multivalued mappings in Banach spaces.
The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties...
A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.
In this paper, two multi-valued versions of the well-known hybrid fixed point theorem of Dhage [6] in Banach algebras are proved. As an application, an existence theorem for a certain differential inclusion in Banach algebras is also proved under the mixed Lipschitz and compactness type conditions.