We discuss, extend, improve and enrich results on simulation functions established by several authors. Furthermore, by using Lemma 2.1 of Radenovic et al. [Bull. Iran. Math. Soc., 2012, 38, 625],we get much shorter and nicer proofs than the corresponding ones in the existing literature.

In this paper, we introduce the concept of coincidence best proximity point for multivalued Suzuki-type $\alpha$ -admissible mapping using $\theta$ -contraction in b-metric space. Some examples are presented here to understand the use of the main results and to support the results proved herein. The obtained results extend and generalize various existing results in literature.

Introduction/purpose: This paper establishes some new results of Piri-Kumam-Dung-type mappings in a complete metric space.The goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F-contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion:The authors believe that the obtained results represent a significant improvement of many known results in the existing literature.

We improve and generalize some new results in fixed point theory in the context of partial b-metric spaces.

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce $(\phi ,F)$ -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping.

In the paper, we consider some fixed point results of $\mathcal{F}$-contractions for triangular $\alpha$-admissible and triangular weak $\alpha$-admissible mappings in metric-like spaces. The results on $\mathcal{F}$-contraction type mappings in the context of metric-like spaces are generalized, improved, unified, and enriched. We prove the main result but using only the property ($\mathcal{F}1$) of the strictly increasing mapping $\mathcal{F}:\left(0,,,+,\infty \right)\to \left(-,\infty ,,,+,\infty \right)$. Our approach gives a proper generalization of several results given in current literature.