scholarly journals The iterative algorithm with inertial and error terms for fixed points of strictly pseudocontractive mappings and zeros of inverse strongly monotone operators

2021 ◽  
Vol 3 (1) ◽  
Keyword(s):  
Fixed Points ◽  
Iterative Algorithm ◽  
Monotone Operators ◽  
Strongly Monotone ◽  
Pseudocontractive Mappings ◽  
Inverse Strongly Monotone ◽  
Error Terms ◽  
Strongly Monotone Operators ◽  
Strictly Pseudocontractive Mappings

scholarly journals Accelerated modified inertial Mann and viscosity algorithms to find a fixed point of $ \alpha - $inverse strongly monotone operators

2021 ◽  
Vol 6 (8) ◽  
pp. 9000-9019
Author(s):  
Hasanen A. Hammad ◽  
◽  
Habib ur Rehman ◽  
Manuel De la Sen ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Monotone Operators ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Operators

scholarly journals Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators

2018 ◽  
Vol 56 (2) ◽  
pp. 13-27 ◽  
Author(s):  
Vasile Berinde
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings ◽  
Strictly Pseudocontractive Mappings ◽  
Nonlinear Mappings

AbstractIn this paper, we introduce and study the class of enriched strictly pseudocontractive mappings in Hilbert spaces and extend some convergence theorems, i.e., Theorem 12 in [Brow-der, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 3.1 in [Marino, G., Xu, H.-K., Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), no. 1, 336–346], from the class of strictly pseudocontractive mappings to that of enriched strictly pseudocontractive mappings and thus include many other important related results from literature as particular cases.

scholarly journals A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-35 ◽  
Author(s):  
Poom Kumam ◽  
Phayap Katchang
Keyword(s):  
Fixed Points ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
General System ◽  
Common Fixed Points ◽  
Iterative Sequence ◽  
Pseudocontractive Mappings ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
Strictly Pseudocontractive Mappings

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others.

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