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.
In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions,...
Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.