Fixed point results for generalized F-contractive and Roger Hardy type F-contractive mappings in G-metric spaces

Very recently, Piri and Kumam (Fixed Point Theory Appl 210:11, 2014) improved the concept of F-contraction due to Wardowski (Fixed Point Theory Appl, 2012) by invoking some weaker conditions on mapping F and established some fixed point results in metric spaces. The purpose of this paper is twofold. Firstly, acknowledging the aforesaid idea of Piri and Kumam, a new generalized F-contraction in the framework of G-metric spaces is defined and by emphasizing the role of generalized F-contraction, a fixed point theorem in the structure of G-metric spaces is proved. Secondly, in the setting of G-metric spaces, Roger Hardy type F-contractive mappings are also defined and employing this, certain fixed point results are presented. Recently, Samet et al. (Int J Anal, 2013) and Jleli et al. (Fixed Point Theory Appl 210:7, 2012) observed that the most of the fixed point results in the structure of G-metric spaces can be obtained from existing literature on usual metric space. Countering this, our aforementioned results in the setting of G-metric spaces cannot be concluded from the existence work in the milieu of associated metric spaces. Our findings are also authenticated with the aid of some appropriate examples.