TY - JOUR JF - IJMSI JO - IJMSI VL - 11 IS - 1 PY - 2016 Y1 - 2016/4/01 TI - Fixed Point Results on $b$-Metric Space via Picard Sequences and $b$-Simulation Functions TT - N2 - In a recent paper, Khojasteh emph{et al.} [F. Khojasteh, S. Shukla, S. Radenovi'c, 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 $mathcal{Z}$-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. SP - 123 EP - 136 AU - Demma, M. AU - Saadati, R. AU - Vetro, P. AD - Iran University of Science and Technology KW - $b$-Metric space KW - Partial order KW - Nonlinear contraction KW - Fixed point KW - $b$-Simulation function. UR - http://ijmsi.ir/article-1-684-en.html DO - 10.7508/ijmsi.2016.01.011 ER -