A fixed point theorem and the Ulam stability in generalized dq-metric spaces
type: Item
instance of: scholarly article
title: A fixed point theorem and the Ulam stability in generalized dq-metric spaces
zbMATH Open document ID: 1402.54037
author: Janusz Brzdȩk
author: Adrian Petruşel
author: E. Karapinar
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-08-15T00:00:00Z
review text: The authors prove a fixed point theorem for \(\Lambda\)-contractive maps in generalized dislocated quasi-metric (simply, dq-metric) spaces. This reduces to the classical Banach contraction principle. It is shown that this theorem can be applied to obtain some results on the Ulam stability of functional equations with one variable taking values in complete quasi-normed spaces, \(p\)-normed spaces, and ultrametric spaces, respectively.
reviewed by: In-Sook Kim
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54E99
zbMATH DE Number: 6918463
zbMATH Keywords: fixed point
zbMATH Keywords: Ulam stability
zbMATH Keywords: dq-metric
zbMATH Keywords: ultrametric
zbMATH Keywords: quasi-norm
zbMATH Keywords: \(p\)-norm
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.07.022
OpenAlex ID: W2883579719
cites work: Stability of functional equations in single variable.
cites work: Metric-like spaces, partial metric spaces and fixed points
cites work: Locally bounded linear topological spaces
cites work: The Stability of Certain Functional Equations
cites work: Q3983330
cites work: Q4938152
cites work: On some recent developments in Ulam's type stability
cites work: Q5264674
cites work: Fixed point theory and the Ulam stability
cites work: A fixed point approach to stability of functional equations
cites work: A fixed point approach to the stability of functional equations in non-Archimedean metric spaces
cites work: On Ulam's type stability of the linear equation and related issues
cites work: Recent developments of the conditional stability of the homomorphism equation
cites work: Fixed points and generalized Hyers-Ulam stability
cites work: Fixed point methods for the generalized stability of functional equations in a single variable
cites work: Nonlinear singular perturbation phenomena: theory and applications
cites work: Applications of fixed point theorems to the Hyers-Ulam stability of functional equations -- a survey
cites work: The associativity equation revisited
cites work: Q4884981
cites work: Q4549797
cites work: Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations
cites work: An answer to a question of Th. M. Rassias and J. Tabor on mixed stability of mappings
cites work: On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings
cites work: Q4658648
cites work: Ψ-Aditive Mappings and Hyers–Ulam Stability
cites work: \(p\)-adic numbers: An introduction.
cites work: A survey of shadowing methods for numerical solutions of ordinary differential equations
cites work: On the asymptoticity aspect of Hyers-Ulam stability of mappings
cites work: Hyers-Ulam-Rassias stability of functional equations in mathematical analysis
cites work: Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis
cites work: On the stability of the linear functional equation in a single variable on complete metric groups
cites work: Q4211216
cites work: Fixed Point Theory in Distance Spaces
cites work: Q5592596
cites work: Q4040882
cites work: On the stability of a functional equation associated with the Fibonacci numbers
cites work: On the stability of functional equations
cites work: Stability has many names
cites work: Q4331453
cites work: Shadowing in dynamical systems
cites work: Hyers-Ulam stability of the linear recurrence with constant coefficients
cites work: Q4012620
cites work: Q4492826
cites work: Q3243449
cites work: Q3406705
cites work: Some fixed point results in dislocated quasi metric (\(dq\)-metric) spaces
cites work: Q3150872
DOI: 10.1016/J.JMAA.2018.07.022
description: scientific article; zbMATH DE number 6918463