On the new Hyers-Ulam-Rassias stability of the generalized cubic set-valued mapping in the incomplete normed spaces
Open Access
- 1 January 2021
- journal article
- research article
- Published by Vilnius University Press in Nonlinear Analysis Modelling and Control
- Vol. 26 (5), 821-841
- https://doi.org/10.15388/namc.2021.26.24367
Abstract
We present a novel generalization of the Hyers-Ulam-Rassias stability definition to study a generalized cubic set-valued mapping in normed spaces. In order to achieve our goals, we have applied a brand new fixed point alternative. Meanwhile, we have obtained a practicable example demonstrating the stability of a cubic mapping that is not defined as stable according to the previously applied methods and procedures.This publication has 19 references indexed in Scilit:
- On orthogonal sets and Banach fixed point theoremFixed Point Theory, 2017
- The Meir–Keeler fixed point theorem in incomplete modular spaces with applicationJournal of Fixed Point Theory and Applications, 2017
- Orthogonal sets: The axiom of choice and proof of a fixed point theoremJournal of Fixed Point Theory and Applications, 2016
- On the stability of the generalized cubic set-valued functional equationApplied Mathematics Letters, 2014
- On the stability of the linear functional equation in a single variable on complete metric groupsJournal of Global Optimization, 2013
- Hyers-Ulam stability of a generalized additive set-valued functional equationJournal of Inequalities and Applications, 2013
- On the stability of set-valued functional equations with the fixed point alternativeFixed Point Theory and Applications, 2012
- Hyers–Ulam stability of additive set-valued functional equationsApplied Mathematics Letters, 2011
- On the stability of an n-dimensional cubic functional equationJournal of Mathematical Analysis and Applications, 2007
- The stability of a cubic type functional equation with the fixed point alternativeJournal of Mathematical Analysis and Applications, 2005