Gholamreza Heidary Joonaghany - Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Ali Farajzadeh - Department of Mathematics, Faculty of Science, University of Razi, Kermanshah ۶۷۱۴۹, Iran.
Mahdi Azhini - Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Farshid Khojasteh - Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad University, Arak, Iran.

In this paper, a new stratification of mappings, which is  called $Psi$-simulation functions, is introduced  to enhance the study of the Suzuki type weak-contractions. Some well-known results in weak-contractions fixed point theory are generalized by our researches. The methods have been appeared in proving the main results are new and different from the usual methods. Some suitable examples are furnished to demonstrate the validity of the hypothesis of our results and reality of our generalizations.

Common fixed point, Suzuki type contractions, Generalized $Psi$-simulation functions