*Article* **Ample Spectrum Contractions and Related Fixed Point Theorems**

#### **Antonio Francisco Roldán López de Hierro 1,\* and Naseer Shahzad 2**


Received: 28 September 2019; Accepted: 28 October 2019; Published: 2 November 2019

**Abstract:** Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. *R*-functions, (*<sup>R</sup>*, S)-contractions and (A, S)-contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.

**Keywords:** *R*-function; simulation function; manageable function; fixed point; contractivity condition; binary relation
