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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.


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

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

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

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


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

Export citation


  • V.A. Faiziev, P. K. Sahoo, On the stability of the quadratic equation on groups, Bull. Belgian Math. Soc., 1 (2007), 1-15.
  • R.Ger, P. Semrl, The stability of the exponential equation, Proc. Am. Math. Soc., 124 (1996), 779–787.
  • A. Grabiec, The generalized Hyers–Ulam stability of a class of functional equations, Publ. Math. Debrecen, 48 (1996), 217–235.
  • D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222-224.
  • S.-M. Jung, P. K. Sahoo, On the stability of a functional equation of Drygas, Aequat. Math., 64 (2002), 263-273.
  • S.-M. Jung, On the stability of gamma functional equation, Result. Math., 33 (1998), 306–309.
  • S.-M. Jung, Hyers Ulam stability of linear differential equations of first order (II), Appl. Math. Lett., 19 (2006), 854-858.
  • I. R. Kachurovskii, On monotone operators and convex functionals, Uspekhi Mat. Nauk., 15 (4) (1960), 213-215.
  • G. Minty, Monotone (nonlinear) operators in a Hilbert space, Duke Math. J., 29 1962), 341-346.
  • T. Miura, S. Miyajima, S. -E. Takahasi, Hyers-Ulam stability of linear differential operator with constant coefficients, Math. Nachr., 258 (2003), 90-96.
  • D. Popa, Hyers–Ulam–Rassias stability of the general linear equation, Nonlinear Funct. Anal. Appl., 4 (2002), 581–588.
  • M.M. Vainberg, On the convergence of the method of steepest descent for nonlinear equations, Sibir. Mat. J., 2 (1961), 201-220.
  • E.H. Zarantonello, The closure of the numerical range contains the spectrum, Bull. Amer. Math. Soc., 70 (1964), 771-778.