Neki poznati rezultati iz nepokretne tačke u kompleksnom domenu: istraživanje
Sažetak
U ovom preglednom radu razmatrani su neki poznati rezultati iz teorije nepokretne tačke nad kompleksnim domenom. Istraživanje i primena teorije nepokretne tačke u kompleksnoj analizi započeti su 1926, godine. Teorema Denjoy-Wolf, zajedno sa Banahovim principom kontrakcije, jedno je od glavnih oruđa (rezultata) matematičke analize.
Reference
Ahlfors, L. 1953. Complex Analysis. New York: McGraw-Hill, 1st ed.
Anderson, J.M., & Vasil’ev, A. 2008. Lower Schwarz-Pick Estimates and Angular Derivatives. Ann. Acad. Sci. Fennicae Math., 33, pp.101–110. Available at: http://www.acadsci.fi/mathematica/Vol33/AndersonVasilev.html. Accessed: 10.03.2018.
Beardon, A.F. 1990. Iteration of contractions and analytic maps. J. Lond. Math. Soc., s2-41(1), pp.141–150. Available at: https://doi.org/10.1112/jlms/s2-41.1.141.
Beardon, A.F. 1997. The dynamics of contractions. Ergodic Theory and Dynamical Systems, 17(6), pp.1257-1266. Available at: https://doi.org/10.1017/s0143385797086434.
Budzynska, M., Kuczumow, T., & Reich, S. 2012. A Denjoy-Wolff theorem for compact holomorphic mappings in reflexive Banach spaces. J. Math. Anal. Appl. 396(2), pp.504–512. Available at: https://doi.org/10.1016/j.jmaa.2012.06.044.
Budzynska, M., Kuczumow, T., & Reich, S. 2013a. Theorems of Denjoy-Wolff type. Annali di Matematica Pura ed Applicata, 192(4), pp.621–648. Available at: https://doi.org/10.1007/s10231-011-0240-z.
Budzynska, M., Kuczumow, T., & Reich, S. 2013b. A Denjoy-Wolff theorem for compact holomorphic mappings in complex Banach spaces. Annales Academiae Scientiarum Fennicae Mathematica, 38, pp.747-756. Available at: https://doi.org/10.5186/aasfm.2013.3846.
Burckel, R.B. 1981. Iterating analytic self-maps of discs. Am. Math. Monthly, 88(6), pp.396–407. Available at: https://doi.org/10.2307/2321822.
Caratheodory, M. 1960. Theory of functions of a complex variable. Chelsea, New York. Vol. 2, English edition.
Contreras, M.D., Díaz-Madrigal, S., & Pommerenke, C. 2006. On boundary critical points for semigroups of analytic functions. Mathematica Scandinavica, 98(1). Available at: https://doi.org/10.7146/math.scand.a-14987.
Cowen, C.C. 1981. Iteration and the Solution of Functional Equations for Functions Analytic in the Unit Disk. Trans. Amer. Math. Soc., 265, pp.69–95. Available at: https://doi.org/10.1090/S0002-9947-1981-0607108-9.
Cowen, C.C. 2010. Fixed points of functions analytic in the unit disk. In: Conference on complex analysis, University of Illinois, May 22. University of Illinois.
Cowen, C.C., & Pommerenke, Ch. 1982. Inequalities for the Angular Derivative of an Analytic Function in the Unit Disk. J. London Math. Soc., s2-26(2), pp.271–289. Available at: https://doi.org/10.1112/jlms/s2-26.2.271.
Denjoy, A. 1926. Sur l’itération des fonctions analytiques, C.R. Acad. Sci. Paris, Serie 1, 182, pp.255–257 (in French).
Earle, C.J., & Hamilton, R.S. 1970. A fixed point theorem for holomorphic mappings. In S. Chern & S. Smale Eds., Proceeding of Symposia on Pure Mathematics. Providence, Rhode Island: American Mathematical Society (AMS), pp.61-65. Available at: https://doi.org/10.1090/pspum/016.
Goebel, K., Sekowski, T., & Stachura, A. 1980. Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball. Nonlinear Analysis: Theory, Methods & Applications, 4(5), pp.1011–1021. Available at: https://doi.org/10.1016/0362-546X(80)90012-7.
Goebel, K. 1982. Fixed points and invariant domains of holomorphic mappings of the Hilbert ball. Nonlinear Analysis: Theory, Methods & Applications, 6(12), pp.1327–1334. Available at: https://doi.org/10.1016/0362-546X(82)90107-9.
Harris, L.A. 2003. Fixed points of holomorphic mappings for domains in Banach spaces. Abstract and Applied Analysis, 2003(5), pp.261-274. Available at: https://doi.org/10.1155/S1085337503205042.
Hayden, T.L., & Suffridge, T.J. 1971. Biholomorphic maps in Hilbert space have a fixed point. Pacific J. Math., 38(2), pp.419–422. Available at: https://doi.org/10.2140/pjm.1971.38.419.
Hayden, T.L., & Suffridge, T.J. 1976. Fixed points of holomorphic maps in Banach spaces. Proceedings of the American Mathematical Society, 60(1), pp.95-105. Available at: https://doi.org/10.1090/s0002-9939-1976-0417869-3.
Henrici, P. 1969. Fixed points of analytic functions. Technical report NO. CS 137.
Julia, G. 1918. Mémoire sur l’itération des fonctions rationelles. J. Math. Pures Appl., 8, pp.47–295 (in French).
Khatskevich, V., Reich, S., & Shoikhet, D. 1995. Fixed point theorems for holomorphic mappings and operator theory in indefinite metric spaces. Integral Equations and Operator Theory, 22(3), pp.305-316. Available at: https://doi.org/10.1007/bf01378779.
Kuczumow, T. 1984. Common fixed points of commuting holomorphic mappings in Hilbert ball and polydisc. Nonlinear Analysis: Theory, Methods & Applications, 8(5), pp.417-419. Available at: https://doi.org/10.1016/0362-546x(84)90081-6.
Kuczumow, T., Reich, S., & Shoikhet, D. 2001. Fixed Points of Holomorphic Mappings: A Metric Approach. In W.A. Kirk& B. Sims Eds., Handbook of Metric Fixed Point Theory. Dordrecht: Springer Nature, pp.437-515. Available at: https://doi.org/10.1007/978-94-017-1748-9_14.
Lemmens, B., Lins, B., Nussbaum, R., & Wortel, M. 2016. Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces, arXiv: 1410.1056v4 [math. DS].
Mateljević, M. 1998. Holomorphic fixed point theorem on Riemann surfaces. Math. Balkanica, 12(1–2), pp.1–4.
Reich, S., & Shoikhet, D. 1996. Generation theory for semigroups of holomorphic mappings in Banach spaces. Abstract and Applied Analysis, 1(1), pp.1-44. Available at: https://doi.org/10.1155/s1085337596000012.
Rudin, W. 1978. The fixed-point sets of some holomorphic maps. Bull. Malays. Math. Soc., 1, pp.25–28.
Suffridge, T.J. 1974. Common fixed points of commuting holomorphic maps of the hyperball. The Michigan Mathematical Journal, 21(4), pp.309–314. Aalable at: https://doi.org/10.1307/mmj/1029001354.
Wolff, J. 1926. Sur une généralization d'un théorème de Schwartz. C.R. Hebd. Seanc. Acad., . 182, pp.918–920 and 183, pp.500–502 (in French).
Xu, Q., Tang, Y., Yang, T., & Srivastava, H.M. 2016. Schwarz lemma involving the boundary fixed point. Fixed Point Theory and Applications, 2016(1). Available at: https://doi.org/10.1186/s13663-016-0574-8.
Vojnotehnički glasnik omogućava otvoreni pristup i, u skladu sa preporukom CEON-a, primenjuje Creative Commons odredbe o autorskim pravima:
Autori koji objavljuju u Vojnotehničkom glasniku pristaju na sledeće uslove:
- Autori zadržavaju autorska prava i pružaju časopisu pravo prvog objavljivanja rada i licenciraju ga Creative Commons licencom koja omogućava drugima da dele rad uz uslov navođenja autorstva i izvornog objavljivanja u ovom časopisu.
- Autori mogu izraditi zasebne, ugovorne aranžmane za neekskluzivnu distribuciju rada objavljenog u časopisu (npr. postavljanje u institucionalni repozitorijum ili objavljivanje u knjizi), uz navođenje da je rad izvorno objavljen u ovom časopisu.
- Autorima je dozvoljeno i podstiču se da postave objavljeni rad onlajn (npr. u institucionalnom repozitorijumu ili na svojim internet stranicama) pre i tokom postupka prijave priloga, s obzirom da takav postupak može voditi produktivnoj razmeni ideja i ranijoj i većoj citiranosti objavljenog rada (up. Efekat otvorenog pristupa).