In the present paper, we first give two order theoretic proofs for a known fixed point theorem in partially ordered metric spaces and then apply the results to find solutions of trace class operator equations.

We investigate the notion of λ-generalized contractions introduced by Ćirić in uniform spaces endowed with a graph and discuss on the existence and uniqueness of fixed points for this type of contractions using the basic entourages.

The main purpose of this paper is to give a direct proof of an interesting special case of a far-reaching theorem of Arazy [1, 2]. Arazy studied the extreme, exposed, and strongly exposed points in the unit balls of symmetrically normed ideals (of operators) acting on a separable Hilbert space, and he obtained very useful and complete results in [2] on the… (More)

*Correspondence: espinola@us.es 1Dpto. de Análisis Matemático, IMUS (Instituto Matemático de la Universidad de Sevilla), Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain Full list of author information is available at the end of the article Abstract In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued… (More)