F-contractions of Hardy–Rogers-type and application to multistage decision

By Francesca Vetro. 2016

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The study of sufficient and necessary conditions, to establishing the existence and uniqueness of fixed points for self-mappings defined in abstract spaces, is an inexhaustible research field for many researchers in mathematics and applied sciences. The key aspect of this success is the generic fixed point problem x = Tx, where T : X → X is a selfmapping of a space X . It is well known that a wide variety of mathematical and practical problems can be solved by reducing them to an equivalent fixed point problem. In fact, by introducing suitable operators, it is possible to solve an equilibrium problem by searching the fixed points of such operators. Moreover, the solutions of differential equations can be obtained in terms of fixed points of integro-differential operators; also the above solutions sets can be characterized by a stability analysis of fixed points sets. These facts are sufficient motivations to increase the interest of mathematicians to establishing extensions and generalizations of the celebrated Banach fixed point theorem [4], which is universally recognized as the fundamental result of metric fixed point theory, see also [20,21]. In this paper, we continue this study by stating existence and uniqueness fixed point theorems for a self-mapping, in the setting of complete metric spaces and complete ordered metric spaces. More precisely, we work with Hardy–Rogers-type conditions, which represent one of the most interesting generalizations of Banach fixed point theorem; but we combine the original idea of Hardy and Rogers [8] with the recent concept of F -contraction

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4cd21d7eacf3670e5f9b51f4fa5a5ecfef7c2be2