Stability of maximum preserving in multi-Banach lattice by fixed point method with some of homogeneity properties

Document Type : Research Paper

Author

Department of Sciences, Najafabad Branch, Islamic Azad University, Najafabad, Iran.

Abstract

In this research work, we demonstrate the Hyers-Ulam stability for functions that are homogeneous of degree $k$, in multi-Banach lattice by fixed point method.

Keywords

[1] N.K. Agbeko, On optimal averages, Acta Math. Hung. 63 (1994), no. 1, 133–147.
[2] , On the structure of optimal measures and some of its applications, Publ. Math. 46 (1995), no. 1-2, 79–87.
[3] , A stability of maximum preserving functional equations on Banach lattices, Miskolc Math. Notes 13 (2012), no. 2, 187–196.
[4] N.K. Agbeko, The Hyers–Ulam–Aoki type stability of some functional equations on Banach lattices, Bull. Polish Acad. Sci. Math. 63 (2015), no. 2.
[5] N.K. Agbeko and S.S. Dragomir, The extension of some Orlicz space results to the theory of optimal measure, Math. Nachr. 286 (2013), 760–771.
[6] N.K. Agbeko, W. Fechner, and E. Rak, On lattice-valued maps stemming from the notion of optimal average, Acta Math. Hung. 152 (2017), no. 1, 72–83.
[7] N.K. Agbeko and P. Szokol, A generalization of the Hyers-Ulam-Aoki type stability of some Banach lattice-valued functional equation, (2018).
[8] T. Aoki, On the stability of the linear transformation in banach spaces, J. Math. Soc. Japon 2 (1950), 64–66
[9] L. C˘adariu and V. Radu, Fixed points and the stability of jensen’s functional equation, J. Inequal. Pure Appl. Math. 4 (2003), no. 1, 4.
[10] H.G. Dales and M.S. Moslehian, Stability of mappings on multi-normed spaces, Glasgow Math. J. 49 (2007), no. 2, 321–332.
[11] H.G. Dales and M.E. Polyakov, Multi normed spaces and multi-banach algebras, University of Leeds, 2008.
[12] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
[13] S.-M. Jung, M.Th. Rassias, and C. Mortici, On a functional equation of trigonometric type, Appl. Math. Comput. 252 (2015), 294–303.
[14] G.H. Kim, Superstability of the p-radical functional equations related to wilson’s and kim’s equation, Int. J. Nonlinear Anal. Appl. 12 (2021), no. Special Issue, 571–582.
[15] A. Lachouri, A. Ardjouni, N. Gouri, and K. Ali Khelil, Existence and stability analysis for nonlinear ψ-hilfer fractional differential equations with nonlocal integral boundary conditions, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 2617–2633.
[16] M.S. Moslehian, Superstability of higher derivations in multi-banach algebras, Tamsui Oxford J. Math. Sci. 24
(2008), no. 4, 417–427.
[17] M.S. Moslehian, K. Nikodem, and D. Popa, Asymptotic aspect of the quadratic functional equation in multi-normed spaces, J. Math. Anal. Appl. 355 (2009), no. 2, 717–724.
[18] E. Movahednia, C. Park, and J.R. Lee, Hyers stability of lattice derivations, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 3239–3248.
[19] Th. M. Rassias, On the stability of the linear mapping in banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
[20] N. Salehi and S.M.S. Modarres, Stability of maximum preserving quadratic functional equation in banach lattices, Miskolc Math. Notes 17 (2016), no. 1, 581–589.
[21] E. Ta¸sdemir, Stability and periodic nature of a system of difference equations, Int. J. Nonlinear Anal. Appl. 11 (2020), no. 2, 187–198.
[22] S.M. Ulam, A collection of mathematical problems, ser. Interscience Tracts in Pure and Applied Mathematics, vol. 8, New York and London: Interscience Publishers, 1960.
[23] M.R. Velayati and N. Salehi, Stability of maximum preserving functional equation on multi-banach lattice by fixed point method, Fixed Point Theory 21 (2020), no. 1, 363–373.
Volume 14, Issue 3
March 2023
Pages 63-71
  • Receive Date: 12 March 2022
  • Revise Date: 16 May 2022
  • Accept Date: 31 July 2022