Fredholm and Volterra nonlinear possibilistic integral equations

Sorin G. Gal; Ionut T. Iancu

doi:10.24193/subbmath.2021.1.09

Fredholm and Volterra nonlinear possibilistic integral equations

Studia Universitatis Babes-Bolyai Matematica ◽

10.24193/subbmath.2021.1.09 ◽

2021 ◽

Vol 66 (1) ◽

pp. 105-113

Author(s):

Sorin G. Gal ◽

Ionut T. Iancu

Keyword(s):

Integral Equations ◽

Functional Equations ◽

Lebesgue Integral ◽

Nonlinear Functional ◽

Classical Integral

Fredholm and Volterra nonlinear possibilistic integral equations 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.

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INTEGRAL EQUATIONS ON THE HALF-LINE WITH DIFFERENCE KERNELS, AND NONLINEAR FUNCTIONAL EQUATIONS

Mathematics of the USSR-Sbornik ◽

10.1070/sm1975v026n01abeh002468 ◽

1975 ◽

Vol 26 (1) ◽

pp. 31-54 ◽

Cited By ~ 3

Author(s):

N B Engibarjan ◽

A A Arutjunjan

Keyword(s):

Integral Equations ◽

Functional Equations ◽

Half Line ◽

Nonlinear Functional

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The convergence of a new iteration process for the solution of nonlinear functional equations in banach space

Mathematical Notes ◽

10.1007/bf01116447 ◽

1968 ◽

Vol 4 (3) ◽

pp. 680-685

Author(s):

D. K. Lika

Keyword(s):

Banach Space ◽

Functional Equations ◽

Iteration Process ◽

Nonlinear Functional

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Analytic Solutions of a Class of Linear and Nonlinear Functional Equations

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.2001.7487 ◽

2001 ◽

Vol 261 (1) ◽

pp. 168-176 ◽

Cited By ~ 3

Author(s):

Eugenia N. Petropoulou

Keyword(s):

Functional Equations ◽

Analytic Solutions ◽

Nonlinear Functional ◽

Linear And Nonlinear

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Generic properties of nonlinear functional equations

Aequationes Mathematicae ◽

10.1007/bf02189672 ◽

1983 ◽

Vol 26 (1) ◽

pp. 120-121

Author(s):

Witold Jarczyk

Keyword(s):

Functional Equations ◽

Generic Properties ◽

Nonlinear Functional

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Remarks on nonlinear functional equations, III

Illinois Journal of Mathematics ◽

10.1215/ijm/1256059304 ◽

1965 ◽

Vol 9 (4) ◽

pp. 617-622 ◽

Cited By ~ 6

Author(s):

Felix E. Browder

Keyword(s):

Functional Equations ◽

Nonlinear Functional

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On the Fredholm alternative for nonlinear functional equations in Banach spaces

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1972-0301585-9 ◽

1972 ◽

Vol 33 (1) ◽

pp. 55-55 ◽

Cited By ~ 7

Author(s):

Peter Hess

Keyword(s):

Banach Spaces ◽

Functional Equations ◽

Fredholm Alternative ◽

Nonlinear Functional

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Stability analysis of one-leg methods for nonlinear functional differential and functional equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2010.07.009 ◽

2010 ◽

Vol 235 (3) ◽

pp. 817-824 ◽

Cited By ~ 3

Author(s):

Yuexin Yu ◽

Liping Wen

Keyword(s):

Stability Analysis ◽

Functional Equations ◽

Nonlinear Functional ◽

Functional Differential

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Convergence of the New Iterative Method

International Journal of Differential Equations ◽

10.1155/2011/989065 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10 ◽

Cited By ~ 22

Author(s):

Sachin Bhalekar ◽

Varsha Daftardar-Gejji

Keyword(s):

Iterative Method ◽

Functional Equations ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Efficient Technique ◽

Nonlinear Functional ◽

Adomian Decomposition ◽

New Iterative Method ◽

Sufficiency Conditions

A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.

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