Hossein Monfared - Department of Mathematics, Bilehsavar Branch, Islamic Azad University, Bilehsavar, Iran.
Mehdi Asadi - Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
Ali Farajzadeh - Department of Mathematics, Razi University, Kermanshah, ۶۷۱۴۹, Iran.

In this paper, at first, we introduce $alpha_{mu}$-admissible, $Z_mu$-contraction and  $N_{mu}$-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions   via $alpha$-admissible simulation mappings, as well. Our results  can be viewed as extension of the corresponding results in this area.  Moreover, some examples and an application to functional integral equations are given to support the obtained results.

Measure of non-compactness, Simulation functions, $alpha$-admissible mappings, Fixed point