Fixed point theorems for convex-power condensing operators relative to the weak topology and appli- cations to Volterra integral equations

previous :: next

Fixed point theorems for convex-power condensing operators relative to the weak topology and appli- cations to Volterra integral equations

Ravi P. Agarwal, Donal O'Regan, and Mohamed-Aziz Taoudi

Source: J. Integral Equations Appl. Volume 24, Number 2 (2012), 167-181.

First Page: Show

Primary Subjects: 47H10, 47H30

Keywords: Convex-power condensing operators; fixed point theorems; measure of weak noncompactness

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jiea/1340369460
Digital Object Identifier: doi:10.1216/JIE-2012-24-2-167
Mathematical Reviews number (MathSciNet): MR2945800

back to Table of Contents

References

R.P. Agarwal, D. O'Regan and M.A. Taoudi, Browder-Krasnoselskii-type fixed point theorems in Banach spaces, Fixed Point Theory Appl. 2010, 243716.

Mathematical Reviews (MathSciNet): MR2684114

Zentralblatt MATH: 1218.47078

O. Arino, S. Gautier and J.P. Penot, A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkc. Ekvac. 27 (1984), 273-279.

Mathematical Reviews (MathSciNet): MR794756

Zentralblatt MATH: 0599.34008

J. Banaś and J. Rivero, On measures of weak noncompactness, Ann. Mat. Pura Appl. 151 (1988), 213-224.

Mathematical Reviews (MathSciNet): MR964510

Zentralblatt MATH: 0653.47035

Digital Object Identifier: doi:10.1007/BF01762795

D. Bugajewski, On the existence of weak solutions of integral equations in Banach spaces, Comment. Math. Univ. Carolin. 38 (1994), 35-41.

Mathematical Reviews (MathSciNet): MR1292580

Zentralblatt MATH: 0816.45012

M. Cichoń, On solutions of differential equations in Banach spaces, Nonlinear Anal. 60 (2005), 651-667.

Mathematical Reviews (MathSciNet): MR2109151

M. Cichoń, Weak solutions of differential equations in Banach spaces, Discuss. Math. Differential Incl. 15 (1995), 5-14.

Mathematical Reviews (MathSciNet): MR1344523

Zentralblatt MATH: 0829.34051

M. Cichoń and I. Kubiaczyk, Existence theorems for the Hammerstein integral equation, Discuss. Math. Differential Incl. 16 (1996), 171-177.

Mathematical Reviews (MathSciNet): MR1646654

Zentralblatt MATH: 0911.45009

E. Cramer, V. Lakshmiksntham and A.R. Mitchell, On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal. 2 (1978), 169-177.

Mathematical Reviews (MathSciNet): MR512280

Zentralblatt MATH: 0379.34041

Digital Object Identifier: doi:10.1016/0362-546X(78)90063-9

F.S. De Blasi, On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. Roum. 21 (1977), 259-262.

Mathematical Reviews (MathSciNet): MR482402

N. Dunford and J.T. Schwartz, Linear operators, Part I: General theory, Interscience Publishers, New York, 1958.

Mathematical Reviews (MathSciNet): MR1009162

Zentralblatt MATH: 0635.47001

R. Engelking, General topology, Heldermann Verlag, Berlin, 1989.

Mathematical Reviews (MathSciNet): MR1039321

J. García-Falset, Existence of fixed points and measure of weak noncompactness, Nonlinear Anal. 71 (2009), 2625-2633.

Mathematical Reviews (MathSciNet): MR2532788

R.F. Geitz, Pettis integration, Proc. Amer. Math. Soc. 82 (1981), 81-86.

Mathematical Reviews (MathSciNet): MR603606

Zentralblatt MATH: 0506.28007

Digital Object Identifier: doi:10.1090/S0002-9939-1981-0603606-8

I. Kubiaczyk, On a fixed point theorem for weakly sequentially continuous mapping, Discuss. Math. Differential Incl. 15 (1995), 15-20.

Mathematical Reviews (MathSciNet): MR1344524

Zentralblatt MATH: 0832.47046

I. Kubiaczyk and S. Szufla, Kneser's theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math. (Beograd) 46 (1982), 99-103.

Mathematical Reviews (MathSciNet): MR710975

L. Liu, F. Guo, C. Wu and Y. Wu, Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spaces, J. Math. Anal. Appl. 309 (2005), 638-649.

Mathematical Reviews (MathSciNet): MR2154141

Zentralblatt MATH: 1080.45005

Digital Object Identifier: doi:10.1016/j.jmaa.2004.10.069

A.R. Mitchell and C.K.L. Smith, An existence theorem for weak solutions of differential equations in Banach spaces, in Nonlinear equations in abstract spaces, V. Lakshmikantham, ed., Academic Press, New York, 1978.

Mathematical Reviews (MathSciNet): MR502554

Zentralblatt MATH: 0452.34054

D. O'Regan, Weak solutions of ordinary differential equations in Banach spaces, Appl. Math. Lett. 12 (1999), 101-105.

Mathematical Reviews (MathSciNet): MR1663477

–––, Integral equations in reflexive Banach spaces and weak topologies, Proc. Amer. Math. Soc. 124 (1996), 607-614.

Mathematical Reviews (MathSciNet): MR1301043

Zentralblatt MATH: 0844.45009

Digital Object Identifier: doi:10.1090/S0002-9939-96-03154-1

–––, Operator equations in Banach spaces relative to the weak topology, Arch. Math. 71 (1998), 123-136.

Mathematical Reviews (MathSciNet): MR1631480

Zentralblatt MATH: 0918.47053

Digital Object Identifier: doi:10.1007/s000130050243

–––, Fixed point theory for weakly sequentially continuous mappings, Math. Comput. Model. 27 (1998), 1-14.

Mathematical Reviews (MathSciNet): MR1616796

Zentralblatt MATH: 1185.34026

J. Sun and X. Zhang, The fixed point theorem of convex-power condensing operator and applications to abstract semilinear evolution equations, Acta Math. Sinica 48 (2005), 339-446 (in Chinese).

Mathematical Reviews (MathSciNet): MR2160721

A. Szep, Existence theorems for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungar. 6 (1971), 197-203.

Mathematical Reviews (MathSciNet): MR330688

E. Zeidler, Nonlinear functional analysis and its applications, I: Fixed point theorems, Springer-Verlag, New York, 1986.

Mathematical Reviews (MathSciNet): MR816732

Zentralblatt MATH: 0583.47050

Guowei Zhang, Tongshan Zhang and Tie Zhang, Fixed point theorems of Rothe and Altman types about convex-power condensing operator and application, Appl. Math. Comput. 214 (2009), 618-623. \noindentstyle

Mathematical Reviews (MathSciNet): MR2541698

Zentralblatt MATH: 1183.47054

Digital Object Identifier: doi:10.1016/j.amc.2009.04.033

previous :: next

Journal of Integral Equations and Applications