Fixed point theory for compact perturbations of pseudocontractive maps
Some new fixed point results are established for mappings of the form with compact and pseudocontractive.
Some new fixed point results are established for mappings of the form with compact and pseudocontractive.
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.
We present two new models of the dynamics of phytoplankton aggregates. The first one is an individual-based model. Passing to infinity with the number of individuals, we obtain an Eulerian model. This model describes the evolution of the density of the spatial-mass distribution of aggregates. We show the existence and uniqueness of solutions of the evolution equation.
In this work, we establish new Furi–Pera type fixed point theorems for the sum and the product of abstract nonlinear operators in Banach algebras; one of the operators is completely continuous and the other one is -Lipchitzian. The Kuratowski measure of noncompactness is used together with recent fixed point principles. Applications to solving nonlinear functional integral equations are given. Our results complement and improve recent ones in [10], [11], [17].
The paper is concerned with the Nemitskii operator in Hölder spaces. Namely conditions are given to ensure acting, continuity, Lipschitz and differentiability properties.