A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
Mathematics of Operations Research
Strong Convergence of a Proximal-Type Algorithm in a Banach Space
SIAM Journal on Optimization
Bregman Monotone Optimization Algorithms
SIAM Journal on Control and Optimization
A new projection and convergence theorems for the projections in Banach spaces
Journal of Approximation Theory
Existence and Approximation of Fixed Points of Firmly Nonexpansive-Type Mappings in Banach Spaces
SIAM Journal on Optimization
A strong convergence theorem for relatively nonexpansive mappings in a Banach space
Journal of Approximation Theory
Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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In this paper, we note that the main convergence theorem in Zhang et al. (2011) [21] is incorrect and we prove a correction. We also modify Halpern's iteration for finding a fixed point of a strongly relatively nonexpansive mapping in a Banach space. Consequently, two strong convergence theorems for a relatively nonexpansive mapping and for a mapping of firmly nonexpansive type are deduced. Using the concept of duality theorems, we obtain analogue results for strongly generalized nonexpansive mappings and for mappings of firmly generalized nonexpansive type. In addition, we study two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.