In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-φ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly co...

This paper is devoted to study the existence of periodic solutions of the second-order equation x00 1⁄4 f ðt; xÞ; where f is a Carathéodory function, by combining some new properties of Green’s function together with Krasnoselskii fixed point theorem on compression and expansion of cones. As applications, we get new existence results for equations with jumping nonlinearities as well as equation...

In this paper, we establish sufficient conditions for the existence and nonexistence of positive solutions to the following nonlinear fractional differential system ⎪⎪⎨ ⎪⎪⎩ Dαu(t)+a(t) f (t,u,v) = 0 in (0,1) , Dβ v(t)+b(t)g(t,u,v) = 0 in (0,1) , u(0) = 0, u(1) = 0, u′(0) = 0, v(0) = 0, v(1) = 0, v′(0) = 0, (P) where 2 < α ,β 3 , a,b ∈ C ((0,1) , [0,+∞)) and the functions f ,g belong to C ([0,1]...

Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the...

Abstract: This paper provides a quantitative version of the classical image recovery problem to find an -approximate solution of the problem. The rate of asymptotic regularity of the iteration schemas, connected with the problem of image recovery, coincides with the existing optimal and quadratic bounds for Krasnoselskii-Mann iterations. We then provide explicit effective and uniform bounds on ...

We examine the existence and multiplicity of positive solutions for a class nonlinear semipositone fractional differential equations involving integral boundary conditions. The results are obtained in terms different intervals parameters by means Leray-Schauder Guo-Krasnoselskii fixed point theorems. Examples included to verify our main results.

"The purpose of this work is to establish a new generalized form the Krasnoselskii type compression-expansion fixed point theorem for sum an expansive operator and completely continuous one. Applications three non- linear boundary value problems associated second order differential equations coincidence are included illustrate main results."

This paper is devoted to study the existence and stability of mild solutions for semilinear fractional evolution equations with a nonlocal final condition. The analysis based on analytic semigroup theory, Krasnoselskii fixed point theorem, special probability density function. An application time diffusion equation condition also given.

Let T be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to T. A. Burton to show that the totally nonlinear dynamic equation with functional delay x△(t) =−a(t)x3(σ(t))+G ( t, x3(t), x3(t − r(t)) ) , t ∈ T, has a periodic solution. We invert this equation to construct a sum of a compact map and a large contraction, which is sui...