فرهنگ و اندیشه ریاضی

فرهنگ و اندیشه ریاضی

یک سؤال خوب از بین نمی‌رود: نمونه‌ای از پژوهش ریاضی

نوع مقاله : ترجمه

نویسنده
دانشگاه کاشان، دانشکدهٔ علوم ریاضی و کامپیوتر
10.30504/mct.2024.1498.2050
چکیده
‏از نقل داستان این سؤال که ‎«‎آیا نگاشت‌های جا‌به‌جایی روی بازهٔ واحد‏ دارای نقطهٔ ثابت مشترکی هستند‎»‎ استفاده می‌کنیم تا راهبردهایی را نشان دهیم که یک پژوهش ریاضی بر اساس آن‌ها پیش می‌رود.
کلیدواژه‌ها
موضوعات

Brown, R. F., A good question won’t go away: An example of mathematical research, Amer. Math.
Monthly, 128 (2021), no. 1, 62-68.

[1]    Alikhani-Koopaei, A., On common fixed points, periodic points and recurrent points of continuous functions, Int. J. Math., 2003 (2003), 2465–2473.
[2]    Baxter, G.,On fixed points of the composite of commuting functions, Proc. Amer. Math. Soc., 15 (1964), 851–855.
[3]    Block, H., Thielman, H., Commuting polynomials, Quart. J. Math., 2 (1951), 241–243.
[4]    Boronski, J., A note on fixed points of abelian actions in dimension one, Proc. Amer. Math. Soc., 147 (2019), 1653–1655.
[5]    Boyce, W.,Commuting functions with no common fixed points, Trans. Amer. Math. Soc., 137 (1969), 77–92.
[6]    Boyce, W., Γ-compact maps on an interval and fixed points, Trans. Amer. Math. Soc., 160 (1971), 87–102.
[7]    Caffrey, B., Egge, E., Michel, G., Rubin, K., Ver Steegh, J., Domino tilings of Aztec diamonds, Baxter permutations, and snow leopard permutations, Involve 8 (2015), 833–858.
[8]    Cánovas, J., Linero, A., On the dynamics of compositions of commuting interval maps, J. Math. Anal. Appl., 305 (2005), 296–303.
[9]    Chu, S., Moyer, R., On continuous functions, commuting functions and fixed points, Fund. Math., 59 (1966), 91–95.
[10]    Chung, F., Graham, R., Higgett, V., Kleiman, M., The number of Baxter permutations, J. Combin. Theory, 24(1978), 382–394.
[11]    Cohen, H. (1964) On fixed points of commuting functions, Proc. Amer. Math. Soc., 15(1964), 293– 296.
[12]    DeMarr, R., A common fixed point theorem for commuting mappings, Amer. Math. Monthly, 70(1963), 535–537.
[13]    Eustice, D., Holomorphic idempotents and common fixed points on the 2-disk, Mich. Math. J., 19 (1972), 347–352.
[14]    Folkman, J., On functions that commute with full functions, Proc. Amer. Math. Soc., 17 (1966), 383–386.
[15]    Gray, W., Smith, C. , Common fixed points of commuting mappings, Proc. Amer. Math. Soc., 53 (1975), 223–226.
[16] Grinc, H., On common fixed points of commuting triangular maps, Bull. Pol. Acad. Sci. Math., 47 (1999), 61–67.
[17] Grinc, H., Snoha, L., Jungck theorem for triangular maps and related results, Appl. Gen. Topol., 1 (2000), 83–92.
[18] Guibert, O., Linusson, S., Doubly alternating Baxter permutations are Catalan. Discrete Math. 217 (2000): 157–166.
[19] Harper, L., Review of [10], Math. Rev., MR0491652 (82b:05011). [20] Huneke, J., On common fixed points of commuting continuous functions on an interval, Trans.
Amer. Math. Soc., 139 (1969), 371–381. [21] Joichi, J., On functions that commute with full functions and common fixed points, Nieuw. Arch.
Wiss., 14 (1966), 247–251. [22] Jungck, G., Commuting mappings and common fixed points, Amer. Math. Monthly, 73 (1966)„ 735–738. doi.org/10.2307/2313982 [23] Jungck, G., Common fixed points for compatible maps on the unit interval, Proc. Amer. Math. Soc., 115 (1992), 495–499.
[24] Linero, A. , Common fixed points for commuting Cournot maps, Real Anal. Exchange, 28 (2002/3), 121–143.
[25] Maxfield, J., Mourant, W., Common fixed points of commuting continuous functions on the unit interval, Indag. Math., 27(1965), 668–670. [26] McDowell, E. (2009) Coincidence values of commuting functions, Topology Proc., 34 (2009), 365– 384.
[27] Ritt, J. F. , Permutable rational functions, Trans. Amer. Math. Soc., 25 (1923), 399–448. [28] Schwartz, A., Common periodic points of commuting functions, Michigan Math. J., 12 (1965), 353–355.
[29] Tauraso, R., Common fixed points of commuting holomorphic maps of the polydisc which are ex- panding on the torus, Adv. Math., 138 (1998), 92–104.

  • تاریخ دریافت 14 شهریور 1403
  • تاریخ بازنگری 03 آبان 1403
  • تاریخ پذیرش 05 آبان 1403
  • تاریخ انتشار 01 خرداد 1405