Ergodic and fixed point theorems for sequences and nonlinear mappings in a Hilbert space

Abstract: In this paper, we introduce the notion of 2-generalized hybrid sequences, extending the notion of nonexpansive and hybrid sequences introduced and studied in our previous work [Djafari Rouhani B., Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. thesis, YaleUniversity, 1981; and other published in J. Math. Anal. Appl., 1990, 2002, and 2014; Nonlinear Anal., 1997, 2002, and 2004], and prove ergodic and convergence theorems for such sequences in a Hilbert space H. Subsequently, we apply our results to prove new fixed point theorems for 2-generalized hybrid mappings, first introduced in [Maruyama T., Takahashi W., Yao M., Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces, J. Nonlinear Convex Anal., 2011, 12, 185-197] and further studied in [Lin L.-J., Takahashi W., Attractive point theorems and ergodic theorems for nonlinear mappings in Hilbert spaces, Taiwanese J. Math., 2012, 16, 1763-1779], defined on arbitrary nonempty subsets of H.

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Ergodic and fixed point theorems for sequences and nonlinear mappings in a Hilbert space ; volume:51 ; number:1 ; year:2018 ; pages:27-36 ; extent:10 ; Demonstratio mathematica ; 51, Heft 1 (2018), 27-36 (gesamt 10)

Beteiligte, Orts- und Zeitangaben

• Urheber: Rouhani, Behzad Djafari

Weitere Informationen

• DOI: 10.1515/dema-2018-0005
• URN: urn:nbn:de:101:1-2411181455345.826870073077
• Rechteinformation: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 15.08.2025, 07:35 MESZ