Fixed points approximation and solutions of some equilibrium and variational inequalities problems.
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
The purpose of this paper is to prove an existence result for a multivalued Cauchy problem using a fixed point theorem for a multivalued contraction on a generalized complete metric space.
It is proved that: for every Banach space which has uniformly normal structure there exists a with the property: if is a nonempty bounded closed convex subset of and is an asymptotically regular mapping such that where is the Lipschitz constant (norm) of , then has a fixed point in .