On the existence of solution of the equation and a generalized coincidence degree theory. I.
We prove some existence theorems for nonlinear integral equations of the Urysohn type and Volterra type , , where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
We have given several proofs on the existence of the price equilibrium --- via variational inequality --- via degree theory and via Brouwer's theorems.
In this paper we investigate weakly continuous solutions of some integral equations in Banach spaces. Moreover, we prove a fixed point theorem which is very useful in our considerations.
In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.
A simpler proof of a result of Burq [1] is presented.
A characterization of exponentially dichotomic and exponentially stable -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.