Fredholm and Volterra nonlinear possibilistic integral equations

Authors

  • Sorin G. GAL Department of Mathematics and Computer Science, University of Oradea, Universitatii 1, 410087, Oradea, Romania, and Academy of Romanian Scientists Splaiul Independentei No. 54, Bucharest 050094, Romania e-mail: galso@uoradea.ro, galsorin23@gmail.com
  • Ionuț T. IANCU Department of Mathematics and Computer Science, University of Oradea, Universitatii 1, 410087, Oradea, Romania e-mail: ionutz.tudor.iancu@gmail.com https://orcid.org/0000-0002-7625-5144

DOI:

https://doi.org/10.24193/subbmath.2021.1.09

Keywords:

Possibility measure, nonlinear possibilistic integral, Fredholm nonlin- ear possibilistic integral equation, Volterra nonlinear possibilistic integral equa- tion, fixed point theorem, successive approximations.

Abstract

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.

Mathematics Subject Classification (2010): 45B05, 47H10, 28E10, 28A99.

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 approximation by non- linear 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, J. Integral Equations Appl., 31(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. 1-2, 132-141.

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Published

2021-03-30

How to Cite

GAL, S. G., & IANCU, I. T. (2021). Fredholm and Volterra nonlinear possibilistic integral equations. Studia Universitatis Babeș-Bolyai Mathematica, 66(1), 105–113. https://doi.org/10.24193/subbmath.2021.1.09

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