In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.

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 ( φ , 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 F-contractions for triangular α-admissible and triangular weak α-admissible mappings in metric-like spaces. The results on 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 (F1) of the strictly increasing mapping F:0,+∞→−∞,+∞. Our approach gives a proper generalization of several results given in current literature.

Based on the presented study results, it can be concluded that the distribution of tree numbers per diameter degrees (diameter structure) in the four measurements of the compartments 51 and 75, did not change. It was also concluded that one functional dependence could be applied for both compartments N=e5,9·e–0,39*d The result of the above is that also in the following measurements, the diameter structure will remain unchanged, in cases of the same or similar selection cuttings both by the scope and by the distribution of felled trees per diameter classes The primary objective of this type of study is to predict, based on a mathematical model of diameter structure development, effect of the scope of selection cuttings and the number of recruitments on the diameter structure, and the simulation of growth, the distribution of trees per diameter classes in the following measurement or measurements, i.e. to foresee the future development of selection stands

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