Sufficient conditions are given for the existence of positive solutions of a boundary-value problem concerning a second-order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning which is introduced in this paper. The Krasnoselskii fixed point theorem on cones in Banach spaces is used.

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone. 2011 Elsevier Inc. All rights reserved.

We employ the Borsuk-Krasnoselskii antipodal theorem to prove a new fixed point theorem in ordered Banach spaces. Then, the applicability of the result is shown by presenting sufficient conditions for the existence of solutions to initial value problems for first-order difference equations in Banach spaces. To prove that result we shall employ set valued analysis techniques.

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form x (t) + cx (t− τ) = A (t, x(t)) x (t) + f (t, x (t− r1 (t)) , . . . , x (t− rk (t))) .

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern's iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in ...

In this paper, we introduce and study a modified Mann-type algorithm that combines inertial terms for solving common fixed point problems of two countable families nonexpansive mappings in Hilbert spaces. Under appropriate assumptions on the sequences parameters, establish strong convergence result sequence generated by proposed method finding mappings. This can be applied to solve monotone inc...

<p style='text-indent:20px;'>A new strong convergence iterative method for solving a split variational inclusion problem involving bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an scheme comprised of inertial extrapolation step together with the Mann-type step. A theorem iterates generated by given under suitable conditions. I...

Based on the Krasnoselskii theorem, we study the existence, multiplicity and nonexistence of positive solutions of general systems of nonlinear algebraic equations under superlinearity and sublinearity conditions. Systems of nonlinear algebraic equations often arise from studies of differential and difference equations. Our results significantly extend and improve those in the literature. A num...

In this article, we investigate the existence of positive periodic solutions for a class of non-autonomous difference equations. Using the Krasnoselskii fixed point theorem, we establish sufficient criteria that are easily verifiable and that generalize and improve related studies in the literature. Numerical simulations are presented which support our theoretical results for some concrete models.