Concavity of solutions of a 2n-th order problem with symmetry

Abstract

Abstract. In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

Approximating Common Solution of Minimization Problems Involving Asymptotically Quasi-Nonexpansive Multivalued Mappings

“…In this direction, several researchers have obtained different results relating to practical consequences of this field of study in areas such as tomography, quantize design, signal enhancement, signal and image reconstruction, signal and filter synthesis, telecommunications, interpolation, extrapolation, and several others. An instance of the above applications can be seen in [1]. It is a known fact that many interesting problems that dwell in physical systems could be recast as fixed-point problems.…”

An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem

“…There has been a significant amount of work published utilizing Avery fixed point theorems to prove the existence of solutions, typically positive solutions, to differential, difference and dynamic equations with varying types of boundary conditions. For a small sample see, [1,2,10,7,11,16,17]. In this paper, we will apply the Avery fixed point theorem, [4], to a second order boundary value problem with antiperiodic boundary conditions to prove the existence of an antisymmetric solution in the sense that x(t) = −x(n − t) for t ∈ [0, n].…”