On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B
Generalized monotone bifunctions and equilibrium problems
Journal of Optimization Theory and Applications
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
Approximating solutions of maximal monotone operators in Hilbert spaces
Journal of Approximation Theory
Differential Inclusions: Set-Valued Maps and Viability Theory
Differential Inclusions: Set-Valued Maps and Viability Theory
Viscosity methods for zeroes of accretive operators
Journal of Approximation Theory
The prox-Tikhonov regularization method for the proximal point algorithm in Banach spaces
Journal of Global Optimization
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An implicit algorithm for finding common fixed points of an uncountable family of nonexpansive mappings is proposed. A new inexact iteration method is also proposed for countable family of nonexpansive mappings. Several strong convergence theorems based on our main results are established in the setting of Banach spaces. Both algorithms are applied for finding zeros of accretive operators and for solving convex minimization, split feasibility and equilibrium problems.