Fixed Point Results on b-Metric Space via Picard Sequences and b-Simulation Functions

In a recent paper, Khojasteh et al. [F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), 1189-1194] presented a new class of simulation functions, say Z-contractions, with unifying power over known contractive conditions in the literature. Following this line of research, we extend and generalize their results on a b-metric context, by giving a new notion of b-simulation function. Then, we prove and discuss some fixed point results in relation with existing ones.