Fixed point results for ordered S-G-contractions in ordered metric spaces - Vetro, Francesca (Nonlinear Analysis: Modelling and Control, 2018)
In this paper, we prove existence and uniqueness of fixed point in the setting of ordered metric spaces. Precisely, we combine the recent notions of (F,φ)-contraction and Z-contraction in order to introduce the notion of ordered S-G-contraction. Then we use the notion of ordered S-G-contraction to show existence and uniqueness of fixed point. We stress that the notion of ordered S-G-contraction includes different types of ordered contractive conditions in the existing literature. Also, we give some examples and additional results in ordered partial metric spaces to support the new theory.