Skip to main content
Log in

Existence, uniqueness and successive approximations for a class of integral-functional equations

  • Research papers
  • Published:
aequationes mathematicae Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Caliuk, Z. B.,On the convergence of the successive approximations (Russian). Trudy Sem. Teor. Differential. Uravnenii s Otklon. Argumentom Družby Narodov Patrisa Lumumby6 (1969), 67–75.

    Google Scholar 

  2. Collatz, L.,Functionalanalysis und numerische Mathematik. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964.

    Google Scholar 

  3. Jankowski, T. andKwapisz, M.,On the existence and uniqueness of solutions of systems of differential equations with a deviated argument. Ann. Polon. Math.25 (1972), 253–277.

    Google Scholar 

  4. Krasnosielski, M. A., Vainikko, G. M., Zabreiko, P. P., Rutickii, I. B., andStecenko, V. J.,On the approximate solutions of operator equations. Moskva 1969 (in Russian).

  5. Kuczma, M.,Functional equations in a single variable. Polish Scientific Publishers, Warszawa, 1968.

    Google Scholar 

  6. Kwapisz, M.,On a certain method of successive approximations and qualitative problems of differential-functional and difference equations in Banach space (Polish). Zeszyty Naukowe Politechniki Gdańskiej, Matematyka IV, Gdańsk, 1965, pp. 3–73.

    Google Scholar 

  7. Kwapisz, M.,On the approximate solutions of an abstract equation. Ann. Polon. Math.19 (1967), 47–60.

    Google Scholar 

  8. Kwapisz, M.,On the existence and uniqueness of solutions of some integralfunctional equation. Ann. Polon. Math. (to appear).

  9. Kwapisz, M. andTuro, J.,On the existence and convergence of successive approximations for some functional equations in a Banach space. J. Differential Equations (to appear).

  10. Opial, Z.,Nonexpansive and monotone mappings in Banach spaces. Center for dynamical systems. Brown University, 1967.

  11. Walter, W.,Differential and integral inequalities. Springer-Verlag, Berlin-New York, 1970.

    Google Scholar 

  12. Walter, W.,Über sukzessive Approximation bei Volterra-Integralgleichungen in mehreren Veränderlichen. Ann. Acad. Sci. Fenn. Ser. A VI,345 (1965), 1–32.

    Google Scholar 

  13. Ważewski, T.,Sur une procédé de prouver la convergence des approximations successive sans utilisation des séries de comparaison. Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys.8 (1960), 45–52.

    Google Scholar 

  14. Žyvotovskii, L. A.,Theorems on the existence and uniqueness classes for solutions of functional equations with hereditary dependence (Russian). Differen. Urav.7 (8) (1971), 1377–1384.

    Google Scholar 

  15. Žyvotovskii, L. A.,On the existence of solutions of differential equations with deviated argument of neutral type (Russian). Differen. Urav.8 (11) (1972), 1936–1942.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kwapisz, M., Turo, J. Existence, uniqueness and successive approximations for a class of integral-functional equations. Aeq. Math. 14, 303–323 (1976). https://doi.org/10.1007/BF01835980

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01835980

AMS (1970) subject classification

Navigation