# Weak and strong topologies and integral equations in Banach spaces

Annales Polonici Mathematici (1995)

- Volume: 61, Issue: 3, page 245-260
- ISSN: 0066-2216

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topDonal O'Regan. "Weak and strong topologies and integral equations in Banach spaces." Annales Polonici Mathematici 61.3 (1995): 245-260. <http://eudml.org/doc/262401>.

@article{DonalORegan1995,

abstract = {The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of $L^α$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.},

author = {Donal O'Regan},

journal = {Annales Polonici Mathematici},

keywords = {Volterra; Hammerstein; existence; integral equations in abstract spaces; weak and strong topologies; Volterra integral equation; Hammerstein integral equation; Banach space; Schauder-Tikhonov fixed point theorem; Krasnosel'skij's fixed point theorem},

language = {eng},

number = {3},

pages = {245-260},

title = {Weak and strong topologies and integral equations in Banach spaces},

url = {http://eudml.org/doc/262401},

volume = {61},

year = {1995},

}

TY - JOUR

AU - Donal O'Regan

TI - Weak and strong topologies and integral equations in Banach spaces

JO - Annales Polonici Mathematici

PY - 1995

VL - 61

IS - 3

SP - 245

EP - 260

AB - The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of $L^α$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.

LA - eng

KW - Volterra; Hammerstein; existence; integral equations in abstract spaces; weak and strong topologies; Volterra integral equation; Hammerstein integral equation; Banach space; Schauder-Tikhonov fixed point theorem; Krasnosel'skij's fixed point theorem

UR - http://eudml.org/doc/262401

ER -

## References

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- [13] G. Gripenberg, S. O. Londen and O. Staffans, Volterra Integral and Functional Equations, Cambridge Univ. Press, New York, 1990. Zbl0695.45002
- [14] R. B. Guenther and J. W. Lee, Some existence results for nonlinear integral equations via topological transversality, J. Integral Equations Appl. 5 (1993), 195-209. Zbl0781.45003
- [15] R. H. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976.
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- [17] K. Yosida, Functional Analysis, Springer, Berlin, 1971.

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