Fixed point theorems for α–ψ-contractive type mappings

By Bessem Samet, Calogero Vetro, Pasquale Vetro. 2012

979 citations recorded by the source corpus.

Abstract In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/478eba8f061ab2edf8d3d52ebcb0acbe799c35d8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

Citations in the corpus

On generalized α-ψ-Geraghty contractions on b-metric spaces (2018, background): “Vetro [29] considered the concept of an admissible mapping to get a very general structure that combines several existing fixed point theorems by introducing α − ψ-contractive type mappings in complete metric spaces.”
New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations (2016, background): “2 in [16].”
Ulam-Hyers Stability Results for Fixed Point Problems via --Contractive Mapping in ()-Metric Space (2013, result): “The presented theorems extend, generalize, and unify several results in the literature, involving the results of Samet et al. (2012).”
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations (2012, background): “After that, many authors established various coupled fixed point theorems (see, for example, [1, 4, 7, 9, 11, 15, 21, 22] and the references cited therein).”
Common fixed points for α-ψ-φ-contractions in generalized metric spaces (2014, methodology): “Following [14], we introduce the notion of f -α-admissible mapping.”
On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory (2017, methodology): “2 in [13] by setting α(p, q) in a proper way.”
Discussion on Contractions on Generalized Metric Spaces (2014, background): “[14] suggested a very interesting class of mappings, α−ψ contraction mappings, to investigate the existence and uniqueness of fixed point.”
ON H+Type Multivalued Contractions and Applications in Symmetric and Probabilistic Spaces (2019, neutral): “[42] coined the notion of α-admissibility.”