Abstract
The purpose of this paper is to present some fixed-point results for single-valued -contractions on ordered and complete gauge space. Our theorems generalize and extend some recent results in the literature. As an application, existence results for some integral equations on the positive real axis are given.
Highlights
Throughout this paper will denote a nonempty set E endowed with a separating gauge structure D {dα}α∈Λ, where Λ is a directed set see 1 for definitions
The purpose of this paper is to present some fixed-point results for single-valued φ-contractions on ordered and complete gauge space
The aim of this paper is to present some fixed-point theorems for φ-contractions on ordered and complete gauge space
Summary
Throughout this paper will denote a nonempty set E endowed with a separating gauge structure D {dα}α∈Λ, where Λ is a directed set see 1 for definitions. Several authors considered the problem of existence and uniqueness of a fixed point for contraction-type operators on partially ordered sets. Pouso, and Rodrguez-Lopez, in a very recent paper, improve some results given by Petrusel and Rus in 4 in the setting of abstract L-spaces in the sense of Frechet, see, for example, 5, Theorems 3.3 and 3.5. Another fixed-point result of this type was given by O’Regan and Petrusel in 6 for the case of φcontractions in ordered complete metric spaces. The aim of this paper is to present some fixed-point theorems for φ-contractions on ordered and complete gauge space. Our theorems generalize the above-mentioned theorems as well as some other ones in the recent literature see; Ran and Reurings 2 , Nieto and Rodrguez-Lopez 3, 7 , Nieto et al 5 , Petrusel and Rus 4 , Agarwal et al 8 , O’Regan and Petrusel 6 , etc
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