• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.881-893
• /
• 2015

In this paper, we introduce the weakly monotone $Pre{\check{s}}i{\acute{c}}$ type mappings in product spaces when the underlying space is an ordered cone metric space. Some fixed point results for such mappings are also proved which generalize and unify several known results in metric and cone metric spaces with normal cone. The results are supported by examples.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.613-629
• /
• 2021

In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on τ-φ-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.