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Generalized common fixed point theorem for generalized hybrid mappings in Hilbert spaces

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Języki publikacji
EN
Abstrakty
EN
In this article, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. From the main theorem, a common fixed point theorem for commutative generalized hybrid mappings is derived as a special case. Our novel approach significantly expands the applicable range of mappings for well-known fixed point theorems to be effective. Examples are presented to explicitly illustrate this contribution.
Wydawca
Rocznik
Strony
752--759
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
  • Department of Economics, Shiga University, Banba 1-1-1, Hikone, Shiga 522-8522, Japan
Bibliografia
  • [1] F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Natl. Acad. Sci. USA 54 (1965), no. 4, 1041.
  • [2] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006.
  • [3] D. Göhde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251–258.
  • [4] F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotonne operators in Banach spaces, Arch. Math. 91 (2008), no. 2, 166–177.
  • [5] T. Igarashi, W. Takahashi and K. Tanaka, Weak convergence theorems for nonspreading mappings and equilibrium problems, in: Nonlinear Analysis and Optimization. S. Akashi, W. Takahashi and T. Tanaka Eds., Yokohama Publishers, Yokohama, 2008, pp. 75–85.
  • [6] F. Kohsaka, Existence and approximation of common fixed points of two hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 16 (2015), no. 11, 2193–2205.
  • [7] M. Hojo, W. Takahashi, and I. Termwuttipong, Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces, Nonlinear Anal. 75 (2012), no. 4, 2166–2176.
  • [8] A. Kondo, Convergence theorems using Ishikawa iteration for finding common fixed points of demiclosed and 2-demi-closed mappings in Hilbert spaces, Adv. Oper. Theory 7 (2022), no. 3, 26
  • [9] A. Kondo, Strong convergence theorems by Martinez-Yanes-Xu projection method for mean-demiclosed mappings in Hilbert spaces, to appear in Rendiconti di Mat. e delle Sue Appl., Sapienza Università di Roma, Italy, 2023.
  • [10] W. Takahashi, Fixed point theorems for new nonlinear mappings in a Hilbert space, J. Nonlinear Convex Anal. 11 (2010), no. 1, 79–88.
  • [11] W. Takahashi and J.-C. Yao, Fixed point theorems and ergodic theorems for nonlinear mappings in Hilbert spaces, Taiwanese J. Math. 15 (2011), no. 2, 457–472.
  • [12] P. Kocourek, W. Takahashi, and J.-C. Yao, Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese J. Math. 14 (2010), no. 6, 2497–2511.
  • [13] K. Aoyama, S. Iemoto, F. Kohsaka, and W. Takahashi, Fixed point and ergodic theorems for λ-hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 11 (2010), no. 2, 335–343.
  • [14] T. Kawasaki and W. Takahashi, Existence and mean approximation of fixed points of generalized hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 14 (2013), no. 1, 71–87.
  • [15] T. Kawasaki and T. Kobayashi, Existence and mean approximation of fixed points of generalized hybrid non-self mappings in Hilbert spaces, Scientiae Math. Japonicae 77 (2014), no. 1, 13–26.
  • [16] A. Kondo, Fixed point theorem for generic 2-generalizd hybrid mappings in Hilbert spaces, Topol. Meth. Nonlinear Anal. 59 (2022), no. 2B, 833–849.
  • [17] B. D. Rouhani, Ergodic and fixed point theorems for sequences and nonlinear mappings in a Hilbert space, Demonstr. Math. 51 (2018), no. 1, 27–36.
  • [18] W. Takahashi, N.-C. Wong, and J.-C. Yao, Attractive point and weak convergence theorems for new generalized hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 13 (2012), no. 4, 745–757.
  • [19] W. Cholamjiak, S. Suantai, and Y. J. Cho, Fixed points for nonspreading-type multi-valued mappings: existence and convergence results, Ann. Acad. Rom. Sci. Ser. Math. Apll 10 (2018), no. 2, 838–844.
  • [20] P. Cholamjiak and W. Cholamjiak, Fixed point theorems for hybrid multivalued mappings in Hilbert spaces, J. Fixed Point Theory Appl. 18 (2016), no. 3, 673–688.
  • [21] M. Hojo, S. Takahashi, and W. Takahashi, Attractive point and ergodic theorems for two nonlinear mappings in Hilbert spaces, Linear Nonlinear Anal. 3 (2017), no. 2, 275–286.
  • [22] M. Hojo, Attractive point and mean convergence theorems for normally generalized hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 18 (2017), no. 12, 2209–2120.
  • [23] K. Goebel and M. Japon-Pineda, A new type of nonexpansiveness, In: Proceedings of 8th International Conference on Fixed Point Theory and its Applications, Yokohama Publishers, Chiang Mai, 2007.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a441f61e-5310-4e79-b83a-e0a192f6db49
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