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On mappings of higher order and their applications to nonlinear equations
1. | Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Matejki 48/49, 60-769 Poznań, Poland |
2. | Optimization and Control Theory Department, Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland |
References:
[1] |
K. Asano and W. Tutschke, An extended Cauchy-Kovalevskaya problem and its solution in associated spaces, Z. Anal. Anwend., 21 (2002), 1055-1060. |
[2] |
J. Appell and P. P. Zabrejko, "Nonlinear Superposition Operators," Cambridge Tracts in Mathematics, vol. 95, Cambridge University Press, 1990. |
[3] |
M. Borkowski, D. Bugajewski and M. Zima, On some fixed point theorems for generalized contractions and their perturbations, J. Math. Anal. Appl., 367 (2010), 464-475.
doi: 10.1016/j.jmaa.2010.01.014. |
[4] |
H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods, SIAM J. Numer. Anal., 27 (1990), 987-1000.
doi: 10.1137/0727057. |
[5] |
D. Bugajewska, D. Bugajewski and H. Hudzik, $BV_{\phi}$ -solutions of nonlinear integral equations, J. Math. Anal. Appl., 287 (2003), 265-278.
doi: 10.1016/S0022-247X(03)00550-X. |
[6] |
D. Bugajewska, D. Bugajewski and G. Lewicki, On nonlinear integral equations in the space of functions of bounded generalized $\phi$-variation, J. Integral Equations Appl., 21 (2009), 1-20.
doi: 10.1216/JIE-2009-21-1-1. |
[7] |
D. Bugajewski, On $BV$-solutions of some nonlinear integral equations, Integral Equations Operator Theory, 46 (2003), 387-398.
doi: 10.1007/s00020-001-1146-8. |
[8] |
O. Diekmann, Run for your life. A note on the asymptotic speed of propagation of an epidemic, J. Differential Equations, 33 (1979), 58-73.
doi: 10.1016/0022-0396(79)90080-9. |
[9] |
G. M. Fichtenholz, "Differential and Integral Calculus," vol. 2, Fizmatgiz, Moscow, 1959, (in Russian). |
[10] |
S. I. Grossman and R. K. Miller, Perturbation theory for Volterra integrodifferential systems, J. Differential Equations, 8 (1970), 457-474. |
[11] |
S. Heikkilä, M. Kumpulainen and S. Seikkala, On functional improper Volterra integral equations and impulsive differential equations in ordered Banach spaces, J. Math. Anal. Appl., 341 (2008), 433-444.
doi: 10.1016/j.jmaa.2007.10.015. |
[12] |
J.-P. Kauthen, Continuous time collocation methods for Volterra-Fredholm integral equations, Numer. Math., 56 (1989), 409-424.
doi: 10.1007/BF01396646. |
[13] |
D. L. Lovelady, A fixed point theorem, a perturbed differential equation, and a multivariable Volterra integral equation, Trans. Amer. Math. Soc., 182 (1973), 71-83.
doi: 10.1090/S0002-9947-1973-0336263-9. |
[14] |
L. Maligranda and W. Orlicz, On some properties of functions of generalized variation, Monatsh. Math., 104 (1987), 53-65.
doi: 10.1007/BF01540525. |
[15] |
J. Matkowski and J. Miś, On a characterization of Lipschitzian operators of substitution in the space $BV$ , Math. Nachr., 117 (1984), 155-159.
doi: 10.1002/mana.3211170111. |
[16] |
R. K. Miller, On the linearization of Volterra integral equations, J. Math. Anal. Appl., 23 (1968), 198-208.
doi: 10.1016/0022-247X(68)90127-3. |
[17] |
R. K. Miller, Admissibility and nonlinear Volterra integral equations, Proc. Amer. Math. Soc., 25 (1970), 65-71.
doi: 10.1090/S0002-9939-1970-0257674-9. |
[18] |
R. K. Miller, J. A. Nohel and J. S. W. Wong, A stability theorem for nonlinear mixed integral equations, J. Math. Anal. Appl., 25 (1969), 446-449.
doi: 10.1016/0022-247X(69)90247-9. |
[19] |
J. Musielak, "Orlicz Spaces and Modular Spaces," Lecture Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin, 1983. |
[20] |
J. Musielak and W. Orlicz, On generalized variations (I), Studia Math., 18 (1959), 11-41. |
[21] |
M. A. Nashed and J. S. W. Wong, Some variants of a fixed point theorem of Krasnoselskii and applications to nonlinear integral equations, J. Math. Mech., 18 (1969), 767-777. |
[22] |
C. Petalas and T. Vidalis, A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc., 118 (1993), 819-821.
doi: 10.1090/S0002-9939-1993-1132421-2. |
[23] |
W. H. Schikhof, "Ultrametric Calculus. An introduction to $p$-adic Analysis," Cambridge Studies in Advanced Mathematics, vol. 4, Cambridge University Press, 2006. |
show all references
References:
[1] |
K. Asano and W. Tutschke, An extended Cauchy-Kovalevskaya problem and its solution in associated spaces, Z. Anal. Anwend., 21 (2002), 1055-1060. |
[2] |
J. Appell and P. P. Zabrejko, "Nonlinear Superposition Operators," Cambridge Tracts in Mathematics, vol. 95, Cambridge University Press, 1990. |
[3] |
M. Borkowski, D. Bugajewski and M. Zima, On some fixed point theorems for generalized contractions and their perturbations, J. Math. Anal. Appl., 367 (2010), 464-475.
doi: 10.1016/j.jmaa.2010.01.014. |
[4] |
H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods, SIAM J. Numer. Anal., 27 (1990), 987-1000.
doi: 10.1137/0727057. |
[5] |
D. Bugajewska, D. Bugajewski and H. Hudzik, $BV_{\phi}$ -solutions of nonlinear integral equations, J. Math. Anal. Appl., 287 (2003), 265-278.
doi: 10.1016/S0022-247X(03)00550-X. |
[6] |
D. Bugajewska, D. Bugajewski and G. Lewicki, On nonlinear integral equations in the space of functions of bounded generalized $\phi$-variation, J. Integral Equations Appl., 21 (2009), 1-20.
doi: 10.1216/JIE-2009-21-1-1. |
[7] |
D. Bugajewski, On $BV$-solutions of some nonlinear integral equations, Integral Equations Operator Theory, 46 (2003), 387-398.
doi: 10.1007/s00020-001-1146-8. |
[8] |
O. Diekmann, Run for your life. A note on the asymptotic speed of propagation of an epidemic, J. Differential Equations, 33 (1979), 58-73.
doi: 10.1016/0022-0396(79)90080-9. |
[9] |
G. M. Fichtenholz, "Differential and Integral Calculus," vol. 2, Fizmatgiz, Moscow, 1959, (in Russian). |
[10] |
S. I. Grossman and R. K. Miller, Perturbation theory for Volterra integrodifferential systems, J. Differential Equations, 8 (1970), 457-474. |
[11] |
S. Heikkilä, M. Kumpulainen and S. Seikkala, On functional improper Volterra integral equations and impulsive differential equations in ordered Banach spaces, J. Math. Anal. Appl., 341 (2008), 433-444.
doi: 10.1016/j.jmaa.2007.10.015. |
[12] |
J.-P. Kauthen, Continuous time collocation methods for Volterra-Fredholm integral equations, Numer. Math., 56 (1989), 409-424.
doi: 10.1007/BF01396646. |
[13] |
D. L. Lovelady, A fixed point theorem, a perturbed differential equation, and a multivariable Volterra integral equation, Trans. Amer. Math. Soc., 182 (1973), 71-83.
doi: 10.1090/S0002-9947-1973-0336263-9. |
[14] |
L. Maligranda and W. Orlicz, On some properties of functions of generalized variation, Monatsh. Math., 104 (1987), 53-65.
doi: 10.1007/BF01540525. |
[15] |
J. Matkowski and J. Miś, On a characterization of Lipschitzian operators of substitution in the space $BV$ , Math. Nachr., 117 (1984), 155-159.
doi: 10.1002/mana.3211170111. |
[16] |
R. K. Miller, On the linearization of Volterra integral equations, J. Math. Anal. Appl., 23 (1968), 198-208.
doi: 10.1016/0022-247X(68)90127-3. |
[17] |
R. K. Miller, Admissibility and nonlinear Volterra integral equations, Proc. Amer. Math. Soc., 25 (1970), 65-71.
doi: 10.1090/S0002-9939-1970-0257674-9. |
[18] |
R. K. Miller, J. A. Nohel and J. S. W. Wong, A stability theorem for nonlinear mixed integral equations, J. Math. Anal. Appl., 25 (1969), 446-449.
doi: 10.1016/0022-247X(69)90247-9. |
[19] |
J. Musielak, "Orlicz Spaces and Modular Spaces," Lecture Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin, 1983. |
[20] |
J. Musielak and W. Orlicz, On generalized variations (I), Studia Math., 18 (1959), 11-41. |
[21] |
M. A. Nashed and J. S. W. Wong, Some variants of a fixed point theorem of Krasnoselskii and applications to nonlinear integral equations, J. Math. Mech., 18 (1969), 767-777. |
[22] |
C. Petalas and T. Vidalis, A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc., 118 (1993), 819-821.
doi: 10.1090/S0002-9939-1993-1132421-2. |
[23] |
W. H. Schikhof, "Ultrametric Calculus. An introduction to $p$-adic Analysis," Cambridge Studies in Advanced Mathematics, vol. 4, Cambridge University Press, 2006. |
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