Tbilisi Mathematical Journal

A note to establish the Hyers-Ulam stability for a nonlinear integral equation with Lipschitzian kernel

Mohammad Saeed Khan and Dinu Teodorescu

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Abstract

In the stability theory, the nonlinear equations were not so much investigated. In this note we consider the stability of a nonlinear integral equation with Lipschitzian kernel. The approach is based on monotonicity properties of a nonlinear operator.

Note

The authors are thankful to the learned referee for his/her deep observations and their suggestions which greatly helped us to improve the paper significantly.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 3 (2018), 41-45.

Dates
Received: 30 January 2018
Accepted: 10 March 2018
First available in Project Euclid: 3 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1538532025

Digital Object Identifier
doi:10.32513/tbilisi/1538532025

Mathematical Reviews number (MathSciNet)
MR3954193

Subjects
Primary: 45G10: Other nonlinear integral equations
Secondary: 45M10: Stability theory 47G10: Integral operators [See also 45P05] 47H05: Monotone operators and generalizations

Keywords
Hyers-Ulam stability nonlinear integral equation strongly monotone operator real Hilbert space Lipschitz operator

Citation

Khan, Mohammad Saeed; Teodorescu, Dinu. A note to establish the Hyers-Ulam stability for a nonlinear integral equation with Lipschitzian kernel. Tbilisi Math. J. 11 (2018), no. 3, 41--45. doi:10.32513/tbilisi/1538532025. https://projecteuclid.org/euclid.tbilisi/1538532025


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