Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability
Commentationes Mathematicae Universitatis Carolinae (2011)
- Volume: 52, Issue: 2, page 177-190
- ISSN: 0010-2628
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top- Agarwal R., O'Regan D., Sikorska-Nowak A., 10.1017/S0004972708000944, Bull. Austral. Math. Soc. 78 (2008), 507–522. MR2472285DOI10.1017/S0004972708000944
- Aliprantis C.D., Border K.C., Infinite Dimensional Analysis, third edition, Springer, Berlin, 2006. Zbl1156.46001MR2378491
- Ben Amar A., Mnif M., Leray-Schauder alternatives for weakly sequentially continuous mappings and application to transport equation, Math. Methods Appl. Sci. 33 (2010), no. 1, 80–90. Zbl1193.47056MR2591226
- Bugajewski D., On the existence of weak solutions of integral equations in Banach spaces, Comment. Math. Univ. Carolin. 35 (1994), no. 1, 35–41. Zbl0816.45012MR1292580
- Chew T.S., Flordeliza F., On and Henstock-Kurzweil integrals, Differential Integral Equations 4 (1991), 861–868. Zbl0733.34004MR1108065
- Cichoń M., Kubiaczyk I., Sikorska A., 10.1023/B:CMAJ.0000042368.51882.ab, Czechoslovak. Math. J. 54 (129) (2004), 279–289. MR2059250DOI10.1023/B:CMAJ.0000042368.51882.ab
- Cichoń M., Weak solutions of differential equations in Banach spaces, Discuss. Math. Differential Incl. 15 (1995), 5–14. MR1344523
- Cichoń M., Kubiaczyk I., 10.1007/BF01189827, Arch. Math. (Basel) 63 (1994), 251–257. MR1287254DOI10.1007/BF01189827
- Cramer E., Lakshmikantham V., Mitchell A.R., On the existence of weak solution of differential equations in nonreflexive Banach spaces, Nonlinear Anal. 2 (1978), 169–177. MR0512280
- DeBlasi F.S., On a property of the unit sphere in Banach space, Bull. Math. Soc. Sci. Math. R.S. Roumanie (NS) 21 (1977), 259–262. MR0482402
- Diestel J., Uhl J.J., Vector Measures, Mathematical Surveys, 15, American Mathematical Society, Providence, R.I., 1977. Zbl0521.46035MR0453964
- Di Piazza L., Kurzweil-Henstock type integration on Banach spaces, Real Anal. Exchange 29 (2003/04), no. 2, 543–555. Zbl1083.28007MR2083796
- Dugundji J., Topology, Allyn and Bacon, Inc., Boston, 1966. Zbl0397.54003MR0193606
- Federson M., Bianconi R., Linear integral equations of Volterra concerning Henstock integrals, Real Anal. Exchange 25 (1999/00), 389–417. Zbl1015.45001MR1758896
- Federson M., Táboas P., 10.1016/S0362-546X(01)00769-6, Nonlinear Anal. 50 (1998), 389–407. MR1906469DOI10.1016/S0362-546X(01)00769-6
- Gamez J.L., Mendoza J., On Denjoy-Dunford and Denjoy-Pettis integrals, Studia Math. 130 (1998), 115–133. Zbl0971.28009MR1623348
- Gordon R.A., 10.1216/rmjm/1181072923, Rocky Mountain J. Math. (21) (1991), no. 3, 923–949. MR1138145DOI10.1216/rmjm/1181072923
- Gordon R.A., The Integrals of Lebesgue, Denjoy, Perron and Henstock, Graduate Studies in Mathematics, 4, American Mathematical Society, Providence, RI, 1994. Zbl0807.26004MR1288751
- Kelley J., General Topology, D. Van Nostrad Co., Inc., Toronto-New York-London, 1955. Zbl0518.54001MR0070144
- Kubiaczyk I., Szufla S., Kenser's theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), 99–103. MR0710975
- Kubiaczyk I., On the existence of solutions of differential equations in Banach spaces, Bull. Polish Acad. Sci. Math. 33 (1985), 607–614. Zbl0607.34055MR0849409
- Kurtz D.S., Swartz C.W., Theories of Integration: The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and Mcshane, World Scientific, Singapore, 2004. Zbl1072.26005MR2081182
- Martin R.H., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley-Interscience, New York-London-Sydney, 1976. Zbl0333.47023MR0492671
- Mitchell A.R., Smith C., An existence theorem for weak solutions of differential equations in Banach spaces, in Nonlinear Equations in Abstract Spaces (Proc. Internat. Sympos., Univ. Texas, Arlington, Tex, 1977), pp. 387–403, Academic Press, New York, 1978. Zbl0452.34054MR0502554
- Lakshmikantham V., Leela S., Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford-New York, 1981. Zbl0456.34002MR0616449
- Lee P.Y., Lanzhou Lectures on Henstock Integration, Series in Real Analysis, 2, World Scientific, Teaneck, NJ, 1989. Zbl0699.26004MR1050957
- Liu L., Guo F., Wu C., Wu Y., 10.1016/j.jmaa.2004.10.069, J. Math. Anal. Appl. 309 (2005), 638–649. Zbl1080.45005MR2154141DOI10.1016/j.jmaa.2004.10.069
- O'Regan D., 10.1007/s000130050243, Arch. Math. (Basel) 71 (1998), 123–136. Zbl0918.47053MR1631480DOI10.1007/s000130050243
- Rudin W., Functional Analysis, 2nd edition, McGraw-Hill, New York, 1991. Zbl0867.46001MR1157815
- Satco B., 10.1007/s10587-006-0078-5, Czechoslovak Math. J. 56(131) (2006), 1029–1047. MR2261675DOI10.1007/s10587-006-0078-5
- Satco B., 10.7151/dmdico.1066, Discuss. Math. Differ. Incl. Control Optim. 26 (2006), 87–101. Zbl1131.45001MR2330782DOI10.7151/dmdico.1066
- Satco B., 10.1016/j.jmaa.2007.02.050, J. Math. Anal. Appl. 336 (2007), 44–53. Zbl1123.45004MR2348489DOI10.1016/j.jmaa.2007.02.050
- Schwabik S., The Perron integral in ordinary differential equations, Differential Integral Equations 6 (1993), 863–882. Zbl0784.34006MR1222306
- Schwabik S., Guoju Y., Topics in Banach Space Integration, World Scientific, Hackensack, NJ, 2005. Zbl1088.28008MR2167754
- Sikorska A., Existence theory for nonlinear Volterra integral and differential equations, J. Inequal. Appl. 6 (3) (2001), 325–338. Zbl0992.45006MR1889019
- Sikorska-Nowak A., Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals, Demonstratio Math. 35 (2002), no. 1, 49–60. Zbl1011.34066MR1883943
- Sikorska-Nowak A., 10.4064/ap83-3-7, Ann. Polon. Math. 83 (2004), no. 3,257–267. Zbl1101.45006MR2111712DOI10.4064/ap83-3-7
- Sikorska-Nowak A., The existence theory for the differential equation in Banach spaces and Henstock-Kurzweil integral, Demonstratio Math. 40 (2007), no. 1, 115–124. Zbl1128.34037MR2330370
- Sikorska-Nowak A., 10.7151/dmdico.1087, Discuss. Math. Differ. Incl. Control Optim. 27 (2007), 315–327. Zbl1149.34053MR2413816DOI10.7151/dmdico.1087
- Sikorska-Nowak A., Existence of solutions of nonlinear integral equations and Henstock-Kurzweil integrals, Comment. Math. Prace Mat. 47 (2007), no. 2, 227–238. Zbl1178.45016MR2377959
- Sikorska-Nowak A., Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces, J. Appl. Math. 2007, article ID 31572, 12 pp. Zbl1148.26010MR2317885
- Sikorska-Nowak A., Nonlinear integral equations in Banach spaces and Henstock-Kurzweil-Pettis integrals, Dynam. Systems Appl. 17 (2008), 97–107. Zbl1154.45011MR2433893
- Szufla S., Kneser's theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 407–413. Zbl0384.34039MR0492684
- Szufla S., Sets of fixed points of nonlinear mappings in functions spaces, Funkcial. Ekvac. 22 (1979), 121–126. MR0551256
- Szufla S., On the application of measure of noncompactness to existence theorems, Rend. Sem. Mat. Univ. Padova 75 (1986), 1–14. Zbl0589.45007MR0847653
- Szufla S., 10.1017/S0004972700003646, Bull. Austral. Math. Soc. 36 (1987), 353–360. Zbl0619.45003MR0923817DOI10.1017/S0004972700003646