A strong convergence theorem for relatively nonexpansive mappings in a Banach space
Journal of Approximation Theory
Strong convergence of the CQ method for fixed point iteration processes
Nonlinear Analysis: Theory, Methods & Applications
A new projection and convergence theorems for the projections in Banach spaces
Journal of Approximation Theory
Journal of Approximation Theory
Journal of Computational and Applied Mathematics
Approximate generalized proximal-type method for convex vector optimization problem in Banach spaces
Computers & Mathematics with Applications
A modified extragradient method for inverse-monotone operators in Banach spaces
Journal of Global Optimization
Approximating zeros of monotone operators by proximal point algorithms
Journal of Global 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
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings
Computers & Mathematics with Applications
Halpern-type iterations for strongly relatively nonexpansive mappings in Banach spaces
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
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In this paper, we study strong convergence of the proximal point algorithm. It is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator, but it fails to converge strongly. Then, in [Math. Program., 87 (2000), pp. 189--202], Solodov and Svaiter introduced the new proximal-type algorithm to generate a strongly convergent sequence and established a convergence property for it in Hilbert spaces. Our purpose is to extend Solodov and Svaiter's result to more general Banach spaces. Using this, we consider the problem of finding a minimizer of a convex function.