Some new convergence theorems and fixed point theorems for MT-functions

2021 ◽  
Vol 9 (1) ◽  
pp. 67-76
Author(s):  
Jen-Yuan Chen ◽  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Convergence Theorems

Fixed point theorems and convergence theorems for some monotone generalized nonexpansive mappings

2020 ◽  
Vol 36 (2) ◽  
pp. 199-204
Author(s):  
M. R. ALFURAIDAN ◽  
M. A. KHAMSI ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Coincidence Fixed Point

We present some new coincidence fixed point theorems for generalized multi-valued weak Γ-contraction mappings. Our outcomes extend several recent results in the framework of complete metric spaces endowed with a graph. Two illustrative examples are included and some consequences are derived.

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

2018 ◽  
Vol 51 (1) ◽  
pp. 27-36
Author(s):  
Behzad Djafari Rouhani
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Ergodic Theorems ◽  
Convergence Theorems ◽  
Nonlinear Anal ◽  
Attractive Point ◽  
Nonlinear Mappings

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.

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