Regular operator convergence and nonlinear equations involving numerical ranges
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- by Ram U. Verma PDF
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Abstract:
Regular operator approximation theory, based on the work of Anselone and Lei (1986), is generalized to the case of strongly accretive operators and applied to nonlinear equations involving the generalized Zarantonello numerical rangesReferences
- Philip M. Anselone, Collectively compact operator approximation theory and applications to integral equations, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. With an appendix by Joel Davis. MR 0443383
- P. M. Anselone and R. Ansorge, Compactness principles in nonlinear operator approximation theory, Numer. Funct. Anal. Optim. 1 (1979), no. 6, 589–618. MR 552242, DOI 10.1080/01630567908816036
- P. M. Anselone and R. Ansorge, A unified framework for the discretization of nonlinear operator equations, Numer. Funct. Anal. Optim. 4 (1981/82), no. 1, 61–99. MR 641830, DOI 10.1080/01630568108816106
- P. M. Anselone and Jin Gan Lei, The approximate solution of monotone nonlinear operator equations, Rocky Mountain J. Math. 16 (1986), no. 4, 791–801. MR 871036, DOI 10.1216/RMJ-1986-16-4-791
- P. M. Anselone and Jin Gan Lei, Nonlinear operator approximation theory based on demi-regular convergence, Acta Math. Sci. (English Ed.) 6 (1986), no. 2, 121–132. MR 924656, DOI 10.1016/S0252-9602(18)30518-6
- R. Ansorge and J. Lei, The convergence of discretization methods if applied to weakly formulated problems. Theory and examples, Z. Angew. Math. Mech. 71 (1991), no. 7-8, 207–221 (English, with German and Russian summaries). MR 1121485, DOI 10.1002/zamm.19910710702
- Kendall E. Atkinson, The numerical solution of a bifurcation problem, SIAM J. Numer. Anal. 14 (1977), no. 4, 584–599. MR 448859, DOI 10.1137/0714038
- Rolf Dieter Grigorieff, Über diskrete Approximationen nichtlinearer Gleichungen 1. Art, Math. Nachr. 69 (1975), 253–272. MR 415439, DOI 10.1002/mana.19750690123
- M. A. Krasnosel′skiĭ, G. M. Vaĭnikko, P. P. Zabreĭko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate solution of operator equations, Wolters-Noordhoff Publishing, Groningen, 1972. Translated from the Russian by D. Louvish. MR 0385655, DOI 10.1007/978-94-010-2715-1
- M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, A Pergamon Press Book, The Macmillan Company, New York, 1964. Translated by A. H. Armstrong; translation edited by J. Burlak. MR 0159197
- M. M. Vaĭnberg, Variatsionnyĭ metod i metod monotonnykh operatorov v teorii nelineĭnykh uravneniĭ, Izdat. “Nauka”, Moscow, 1972 (Russian). MR 0467427
- Ram U. Verma, On the external approximation-solvability of nonlinear equations, Panamer. Math. J. 2 (1992), no. 3, 23–42. MR 1173147
- Ram U. Verma, Phi-stable operators and inner approximation-solvability, Proc. Amer. Math. Soc. 117 (1993), no. 2, 491–499. MR 1127144, DOI 10.1090/S0002-9939-1993-1127144-X
- Ram U. Verma, General approximation-solvability of nonlinear equations involving $\scr A$-regular operators, Appl. Math. Lett. 6 (1993), no. 2, 31–33. MR 1347771, DOI 10.1016/0893-9659(93)90008-B
- Ram U. Verma, On regular operator approximation theory, J. Math. Anal. Appl. 183 (1994), no. 3, 591–604. MR 1274859, DOI 10.1006/jmaa.1994.1165
- J. R. L. Webb, On a property of duality mappings and the $A$-properness of accretive operators, Bull. London Math. Soc. 13 (1981), no. 3, 235–238. MR 614661, DOI 10.1112/blms/13.3.235
- Eduardo H. Zarantonello, The closure of the numerical range contains the spectrum, Bull. Amer. Math. Soc. 70 (1964), 781–787. MR 173176, DOI 10.1090/S0002-9904-1964-11237-4
- Eberhard Zeidler, Nonlinear functional analysis and its applications. II/B, Springer-Verlag, New York, 1990. Nonlinear monotone operators; Translated from the German by the author and Leo F. Boron. MR 1033498, DOI 10.1007/978-1-4612-0985-0
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1859-1864
- MSC: Primary 47H17; Secondary 45L10, 65J15
- DOI: https://doi.org/10.1090/S0002-9939-1995-1242108-5
- MathSciNet review: 1242108