Study of \Gamma-Simulation Functions, Z_\Gamma-Contractions and Revisiting the L-Contractions

Abstract

In this paper, we introduce the notions of $\mathcal{Z}_{\Gamma}-$contractions and Suzuki $\mathcal{Z}_{\Gamma}$-contractions via ${\Gamma}-$simulation functions. By using these new contractions, we extend and unify several existing fixed point results in the corresponding literature. We also show that the recently defined notion of $\mathscr{L}-$simulation function is an special case of $\mathcal{Z}_{\Gamma}-$contraction. In addition, some notable examples are given to illustrate and support the obtained results.