## Abstract

Using the weakly Picard operators technique we establish existence, data dependence and comparison results of solutions for a functional integral equation with abstract Volterra operators. Some examples which show the importance of our results are also included.

## Authors

D. **Otrocol**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,

Technical University of Cluj-Napoca)

V.** Ilea
**(Babes-Bolyai Univ.)

## Keywords

Functional integral equation, weakly Picard operators, data dependence and abstract Volterra operator

## Cite this paper as:

D. Otrocol, V. Ilea, On the qualitative properties of functional integral equations with abstract Volterra operators, Res. Fixed Point Theory Appl., Vol. 2018 (2018), Article ID 201813, 08 pages,

https://doi.org/10.30697/rfpta-2018-13

## About this paper

##### Journal

Results in Fixed Point Theory and Applications

##### Publisher Name

##### DOI

https://doi.org/10.30697/rfpta-2018-13

##### Print ISSN

2581-6047

##### Online ISSN

##### MR

##### ZBL

## Google Scholar

[1] R.P. Agarwal, S. Arshad, V. Lupulescu, D. O’Regan, *Evolution equations with causal operators*, Differ. Equ. Appl. 7 (2015) No. 1 15-26.

[2] N.V. Azbelev (ed), *Functional-differential equations* (Russian), Perm. Politekh. Inst., Perm, 1985.

[3] C. Corduneanu, *Integral Equations and Stability of Feedback Systems*, Academic Press, New York, 1973.

[4] C. Corduneanu, *Abstract Volterra equations (a survey)*, Math. Comput. Modelling 32 (2000) 1503- 1528.

[5] D. Guo, V. Lakshmikantham, X. Liu, *Nonlinear Integral Equations in Abstract Spaces*, Kluwer Academic Publishers, 1996.

[6] V.A. Ilea, D. Otrocol, *An application of the Picard operator technique to functional integral equations*, J. Nonlinear Convex Anal. 18 (2017) No. 3 405-413

[7] V. Kolmanovskii, A. Myshkis, *Applied Theory of Functional Differential Equations*, Kluwer Academic Publisers, 1992.

[8] V. Lupulescu, *Causal functional differential equations in Banach spaces*, Nonlinear Anal. 69 (2008) No. 12 4787-4795.

[9] V. Muresan, *Some results on the solutions of a functional-integral equation*, Stud. Univ. Babes-Bolyai Math. 56 (2011) No. 4 157-164.

[10] D. O’Regan, *A note on the topological structure of the solution set of abstract Volterra equations*, Mathematical Proceedings of the Royal Irish Academy 99A (1999) No. 1 67-74.

[11] D. Otrocol, *Abstract Volterra operators*, Carpathian J. Math. 24 (2008) No. 3 370-377.

[12] D. Otrocol, V.A. Ilea*, Qualitative properties of a functional differential equation*, Electron. J. Qual. Theory Differ. Equ. (2014) No. 47 1-8.

[13] S. Reich, A.J. Zaslavski, *Almost all nonexpansive mappings are contractive*, C.R. Math. Rep. Acad. Sci. Canada 22 (2000) 118-124

[14] S. Reich, A.J. Zaslavski, *The set of noncontractive mappings is sigma-porous in the space of all nonexpansive mappings*, C.R. Acad. Sci. Paris Ser. I Math. 333 (2001) 539-544.

[15] I.A. Rus, *Picard operators and applications*, Sci. Math. Jpn. 58 (2003) No. 1 191-219.

[16] I.A. Rus, *Generalized Contractions and Applications*, Cluj University Press, 2001.

[17] M.A. Serban, *Data dependence for some functional-integral equations*, J. Appl. Math. 1 (2008) No. 1 219-234.

[18] M.A. Serban, I.A. Rus, A. Petrusel, *A class of abstract Volterra equations, via weakly Picard operators technique*, Math. Inequal. Appl. 13 (2010) 255-269.