Fredholm and Volterra nonlinear possibilistic integral equations
DOI:
https://doi.org/10.24193/subbmath.2021.1.09Keywords:
Possibility measure, nonlinear possibilistic integral, Fredholm nonlinear possibilistic integral equation, Volterra nonlinear possibilistic integral equation, fixed point theorem, successive approximationsAbstract
In this paper we study the nonlinear functional equations obtained from the classical integral equations of Fredholm and of Volterra of second kind, by replacing there the linear Lebesgue integral with the nonlinear possibilistic integral.References
Bede, B., Coroianu, L., Gal, S.G., Approximation by Max-Product Type Operators, Springer, New York, 2016.
De Cooman, G., Possibility theory. I. The measure-and integral-theoretic groundwork, Internat. J. Gen. Systems, 25 (1997), no. 4, 291-323.
Coroianu, L., Gal, S.G., Opris, B., Trifa, S., Feller' s scheme in approxima-
tion by nonlinear possibilistic integral operators, Numer. Funct. Anal.
Optim, 38 (2017), 327-343.
Dubois D., Prade, H., Possibility Theory, Plenum Press, New York, 1988.
Gal, S.G., Fredholm-Choquet integral equations, J. Integral Equations Appl., 31 (2019), no. 2, 183-194.
Gal, S.G., Volterra-Choquet integral equations, Integral Equations Appl.,
(2019), no. 4, 495-504.
Gal, S.G., A possibilistic approach of the max-product Bernstein kind
operators, Results Math., 65 (2014), 453-462.
Gal, S.G., On the laws of large numbers in possibility theory, Ann. Acad. Rom. Sci. Ser. Math. Appl., 11 (2019), no. 2, 274-284.
Gal, S.G., Approximation by polynomial possibilistic integral operators, Ann. Acad. Rom. Sci. Ser. Math. Appl., 12 (2020), no. 1, to appear.