A Fixed Point Result with a Contractive Iterate at a Point

In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the cont...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 7; no. 7; p. 606
Main Authors Alqahtani, Badr, Fulga, Andreea, Karapınar, Erdal
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2019
Subjects
contractive iterate at a point
fixed point
Fixed points (mathematics)
Mapping
Mathematics
Metric space
Operators (mathematics)
Ulam stability
Online AccessGet full text

Cover

More Information
Summary:In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last, the iteration number may vary for each point in the domain of the operator for which we look for a fixed point. Consequently, the proved results generalize the acknowledged results in the field, including the well-known theorems of Seghal, Kincses-Totik, and Banach-Caccioppoli. We present two illustrative examples to support our results. As an application, we consider an Ulam-stability of one of our results.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7070606