Pseudo-Fredholm operators in generator-based ∗-fuzzy measure spaces: Stability and Nyström approximation

Abolhassanifar, M. S.; Saadati, R.; Pazar Varol, B.

doi:10.22111/ijfs.2026.10184

Articles in Press

Document Type : Original Manuscript

Authors

¹ School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran.

² Department of Mathematics, Iran University of Science and Technology, Tehran, Iran

³ Department of Mathematics, Faculty of Arts and Sciences, Kocaeli University, Kocaeli, Turkiye.

https://doi.org/10.22111/ijfs.2026.10184

Abstract

In this paper, we study pseudo-Fredholm equations in generator-based ∗–fuzzy measure spaces. A control radius is defined from the generator and the ∗-fuzzy integral, and a Boyd-Wong-type fixed-point theorem is proved. We obtain residual, inexact-iteration, and data-stability estimates. For the Hamacher triangular norm, the pseudo-Nyström scheme is second- order convergent. Changes of generator, perturbations of the ∗-fuzzy measure, and a bi-scale L¹–L² generator error construction are also considered.

Keywords

References

[1] M. S. Abolhassanifar, R. Saadati, M. B. Ghaemi, R. Mesiar, ∗–Fuzzy martingale and Doob’s maximal inequalities, Fuzzy Sets and Systems, 542 (2026). https://doi.org/10.1016/j.fss.2026.110004

[2] S. Alinia Jildani, H. Agahi, S. M. Vaezpour, Some notes on the pseudo-integrals based on pseudo-operations, Fuzzy Sets and Systems, 533 (2026), 109816. https://doi.org/10.1016/j.fss.2026.109816

[3] D. Barrera, M. Bartoň, I. Chiarella, S. Remogna, On numerical solution of Fredholm and Hammerstein integral equations via Nyström method and Gaussian quadrature rules for splines, Applied Numerical Mathematics, 174 (2022), 71-88. https://doi.org/10.1016/j.apnum.2022.01.009

[4] B. Bede, Approximation by Shepard-type pseudo-linear operators and applications to image processing, International Journal of Approximate Reasoning, 50(1) (2009), 21-36. https://doi.org/10.1016/j.ijar.2008.01.007

[5] B. Bede, D. O’Regan, The theory of pseudo-linear operators, Knowledge-Based Systems, 38 (2013), 19-26. https: //doi.org/10.1016/j.knosys.2012.07.003

[6] A. M. Bica, S. Ziari, Gauss–Legendre type quadrature iterative method for fuzzy Fredholm integral equations, Fuzzy Sets and Systems, 477 (2024), 108823. https://doi.org/10.1016/j.fss.2023.108823

[7] D. W. Boyd, J. S. Wong, On nonlinear contractions, Proceedings of the American Mathematical Society, 20(2) (1969), 458-464. https://doi.org/10.1090/S0002-9939-1969-0239559-9

[8] P. Díaz de Alba, L. Fermo, G. Rodriguez, Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules, Numerische Mathematik, 146 (2020), 699-728. https://doi.org/10. 1007/s00211-020-01163-7

[9] L. Fermo, D. Mezzanotte, D. Occorsio, A global method for solving second-kind Volterra–Fredholm integral equations, BIT Numerical Mathematics, 65 (2025). https://doi.org/10.1007/s10543-025-01061-0

[10] A. Ghaffari, R. Chaharpashlou, The ∗-fuzzy Lebesgue–Radon–Nikodym theorem and differentiation in fuzzy measure theory, Fuzzy Sets and Systems, 523(C) (2026), 109579. https://doi.org/10.1016/j.fss.2025.109579

[11] A. Ghaffari, R. Saadati, R. Mesiar, Inequalities in triangular norm-based ∗-fuzzy (L+)p spaces, Mathematics, 8(11) (2020), 1984. https://doi.org/10.3390/math8111984

[12] A. Ghaffari, R. Saadati, R. Mesiar, Fuzzy number-valued triangular norm-based decomposable time-stamped fuzzy measure and integration, Fuzzy Sets and Systems, 430 (2022), 144-173. https://doi.org/10.1016/j.fss.2021. 03.018

[13] V. Gregori, J. J. Miñana, B. Roig, A. Sapena, On completeness and fixed point theorems in fuzzy metric spaces, Mathematics, 12(2) (2024), 287. https://doi.org/10.3390/math12020287

[14] O. Hadžić, E. Pap, Fixed point theory in probabilistic metric spaces, Mathematics and Its Applications, 536, Kluwer Academic Publishers, Dordrecht, 2001. https://doi.org/10.1007/978-94-017-1560-7

[15] E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Trends in Logic, 8, Kluwer Academic Publishers, Dordrecht, 2000. https://doi.org/10.1007/978-94-015-9540-7

[16] G. Mastroianni, G. Monegato, Truncated quadrature rules over (0,∞) and Nyström-type methods, SIAM Journal on Numerical Analysis, 41 (2003), 1870-1892. https://doi.org/10.1137/S0036142901391475

[17] R. Mesiar, J. Li, E. Pap, Discrete pseudo-integrals, International Journal of Approximate Reasoning, 54(3) (2013), 357-364. https://doi.org/10.1016/j.ijar.2012.07.008

[18] J. J. Miñana, A. Šostak, O. Valero, On metrization of fuzzy metrics and application to fixed point theory, Fuzzy Sets and Systems, 468 (2023), 108625. https://doi.org/10.1016/j.fss.2023.108625

[19] E. Pap, g-Calculus, Review of Research, Faculty of Science, Mathematics Series, University of Novi Sad, 23(1) (1993), 145-156.

[20] E. Pap, Generalized real analysis and its applications, International Journal of Approximate Reasoning, 47(3) (2008), 368-386. https://doi.org/10.1016/j.ijar.2007.05.015

[21] B. E. Rhoades, A comparison of various definitions of contractive mappings, Transactions of the American Mathematical Society, 226 (1977), 257-290. https://doi.org/10.1090/S0002-9947-1977-0433430-4

[22] B. Schweizer, A. Sklar, Probabilistic metric spaces, North-Holland, New York, 1983.

[23] S. Torkaman, M. Heydari, An iterative Nyström-based method to solve nonlinear Fredholm integral equations of the second kind, Applied Numerical Mathematics, 194 (2023), 59-81. https://doi.org/10.1016/j.apnum.2023.08. 009

[24] J. Vanterler da C. Sousa, G. S. F. Frederico, E. C. de Oliveira, ψ-Hilfer pseudo-fractional operator: New results about fractional calculus, Computational and Applied Mathematics, 39 (2020), 254. https://doi.org/10.1007/ s40314-020-01304-6

[25] J. Vanterler da C. Sousa, M. Vellappandi, V. Govindaraj, G. S. F. Frederico, Reachability of fractional dynamical systems using ψ-Hilfer pseudo-fractional derivative, Journal of Mathematical Physics, 62(8) (2021), 082703. https: //doi.org/10.1063/5.0049341

[26] D. Zhang, R. Mesiar, E. Pap, Pseudo-integral and generalized Choquet integral, Fuzzy Sets and Systems, 446 (2022), 193-221. https://doi.org/10.1016/j.fss.2020.12.005

[27] D. Zhang, E. Pap, Fubini theorem and generalized Minkowski inequality for the pseudo-integral, International Journal of Approximate Reasoning, 122 (2020), 9-23. https://doi.org/10.1016/j.ijar.2020.03.010

Iranian Journal of Fuzzy Systems

Pseudo-Fredholm operators in generator-based ∗-fuzzy measure spaces: Stability and Nyström approximation

References

References

Articles in Press, Accepted Manuscript
Available Online from 24 September 2026

Pseudo-Fredholm operators in generator-based ∗-fuzzy measure spaces: Stability and Nyström approximation

References

References

Articles in Press, Accepted Manuscript Available Online from 24 September 2026

Articles in Press, Accepted Manuscript
Available Online from 24 September 2026