# On some nonlinear alternatives of Leray-Schauder type and functional integral equations

Archivum Mathematicum (2006)

- Volume: 042, Issue: 1, page 11-23
- ISSN: 0044-8753

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topDhage, Bapurao Chandra. "On some nonlinear alternatives of Leray-Schauder type and functional integral equations." Archivum Mathematicum 042.1 (2006): 11-23. <http://eudml.org/doc/249780>.

@article{Dhage2006,

abstract = {In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991), 153–196.) and Dhage and Regan (Dhage, B. C. and O’Regan, D., A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ. 7(3-4)(2000), 259–267.).},

author = {Dhage, Bapurao Chandra},

journal = {Archivum Mathematicum},

keywords = {Banach algebra; fixed point theorem; integral equations; Banach algebra; fixed point theorem; integral equation; functional differential equation; initial value problem},

language = {eng},

number = {1},

pages = {11-23},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On some nonlinear alternatives of Leray-Schauder type and functional integral equations},

url = {http://eudml.org/doc/249780},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Dhage, Bapurao Chandra

TI - On some nonlinear alternatives of Leray-Schauder type and functional integral equations

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 1

SP - 11

EP - 23

AB - In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991), 153–196.) and Dhage and Regan (Dhage, B. C. and O’Regan, D., A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ. 7(3-4)(2000), 259–267.).

LA - eng

KW - Banach algebra; fixed point theorem; integral equations; Banach algebra; fixed point theorem; integral equation; functional differential equation; initial value problem

UR - http://eudml.org/doc/249780

ER -

## References

top- Browder F. E., Nonlinear operators and nonlinear equations of evolutions in Banach spaces, Proc. Symp. pure Math. Amer. Math. Soc. Providence, Rhode Island 1976. (1976) MR0405188
- Chandrasekhar S., Radiative Heat Transfer, Dover, New York, 1960. (1960) MR0111583
- Deimling K., Nonlinear Functional Analysis, Springer Verlag, 1985. (1985) Zbl0559.47040MR0787404
- Dhage B. C., On some variants of Schauder’s fixed point principle and applications to nonlinear integral equations, J. Math. Phys. Sci. 25 (1988), 603–611. (1988) Zbl0673.47043MR0967242
- Dhage B. C., A fixed point theorem and applications to nonlinear integral equations, Proc. Internat. Symp. Nonlinear Anal. Appl. Bio-Math., Waltair, India (1987), 53–59. (1987)
- Dhage B. C., On $\alpha $-condensing mappings in Banach algebras, The Math. Student 6 (1994), 146–152. (1994) Zbl0882.47033MR1292381
- Dhage B. C., On a fixed point theorem of Krasnoselskii type, Electron. J. Qual. Theory Differ. Equ. 2002, No. 6, 9 pp. (electronic). MR1895277
- Dhage B. C., Ntouyas S. K., Existence results for nonlinear functional integral equations via a fixed point theorem of Krasnoselskii-Schaefer type, Nonlinear Studies 9(3)(2002), 307–317. MR1918909
- Dhage B. C., Jahagirdar P. G., On nonlinear integral equations in Banach algebras, Applied Sciences Periodical II (2000), 131–133. MR1840872
- Dhage B. C., O’Regan D., A fixed point theorem in Banach algebras with applications to functional integral equations, Funct. Differ. Equ. 7(3-4)(2000), 259–267. Zbl1040.45003MR1940503
- Dugundji J., Granas A., Fixed point theory, Monographie Matematyczne, Warsaw, 1982. (1982) Zbl0483.47038
- Granas A., Guenther R. B., Lee J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991), 153–196. (1991) MR1103033
- Nashed M. Z., Wong J. S. W., Some variants of a fixed point theorem of Krasnoselskii and applications to nonlinear integral equations, J. Math. Mech. 18 (1969), 767–777. (1969) MR0238140
- Ntouyas S. K., Tsamatos P. G., A fixed point theorem of Krasnoselskii-nonlinear alternative type with applications to functional integral equations, Differential Equations Dynam. Systems 7(2) (1999), 139–146. (1999) MR1860784
- Subramanyam P. V., Sundarsanam S. K., A note on functional integral equations, Differential Equations Dynam. Systems 4 (1996), 473–478. (1996)
- Zeidler E., Nonlinear Functional Analysis and Its Applications I, Springer Verlag, 1985. (1985) MR0816732

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