A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions

Q Dong, D Jiang, P Cholamjiak, Y Shehu - Journal of Fixed Point Theory …, 2017 - Springer
Our interest in this paper is to prove a strong convergence result for finding a zero of the sum
of two monotone operators, with one of the two operators being co-coercive using an …

Nonlinear operators of monotone type and convergence theorems with equilibrium problems in Banach spaces

W Takahashi, JC Yao - Taiwanese Journal of Mathematics, 2011 - projecteuclid.org
Our purpose in this paper is first to discuss nonlinear operators and nonlinear projections in
Banach spaces which are related to the resolvents of $ m $-accretive operators and maximal …

Weak and strong convergence theorems for positively homogenuous nonexpansive mappings in Banach spaces

W Takahashi, JC Yao - Taiwanese Journal of Mathematics, 2011 - projecteuclid.org
Our purpose in this paper is first to prove a weak convergence theorem by Mann's iteration
for positively homogeneous nonexpansive mappings in a Banach space. Further, using the …

Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a countable family of nonexpansive mappings

U Kamraksa, R Wangkeeree - Journal of Global Optimization, 2012 - Springer
In this paper, we introduce the new generalized mixed equilibrium problem basing on
hemicontinuous and relaxed monotonic mapping. Using the KKM technique, we obtain the …

[PDF][PDF] A NEW HYBRID HALPERN-BASED EXTRAGRADIENT ALGORITHM FOR A PSEUDOMONOTONE EQUILIBRIUM PROBLEM AND A FIXED POINT PROBLEM …

Y SHI, Z ZHU - Journal of Applied & Numerical Optimization, 2024 - jano.biemdas.com
In this paper, we propose a hybrid Halpern-based extragradient algorithm for finding a
common solution of a pseudomonotone equilibrium problem and a fixed point problem of a …

[HTML][HTML] Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

P Cholamjiak, S Suantai - Computers & Mathematics with Applications, 2011 - Elsevier
We prove the existence of a solution of the mixed equilibrium problem (MEP) by using the
KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid …

[HTML][HTML] Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

H Dehghan - Applied Mathematics Letters, 2011 - Elsevier
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a
uniformly convex and smooth Banach space is proved by using metric projections. This …

[PDF][PDF] Weak and strong convergence theorems for commutative families of positively homogeneous nonexpansive mappings in Banach spaces

W Takahashi, NC Wong, JC Yao - J. Nonlinear Convex Anal, 2014 - academia.edu
In this paper, we first prove a weak convergence theorem by Mann's iteration for a
commutative family of positively homogeneous nonexpansive mappings in a Banach space …

[PDF][PDF] Some characterizations for a family of nonexpansive mappings and convergence of a generated sequence to their common fixed point

Y Kimura, K Nakajo - Fixed Point Theory and Applications, 2009 - Springer
Motivated by the method of Xu (2006) and Matsushita and Takahashi (2008), we
characterize the set of all common fixed points of a family of nonexpansive mappings by the …

[PDF][PDF] Hybrid projection algorithms for total asymptotically strict quasi-φ-pseudocontracions

XZM Wang, J Yang - J. Nonlinear Sci. Appl, 2015 - kurims.kyoto-u.ac.jp
The purpose of this article is to prove strong convergence theorems for total asymptotically
strict quasi-φ-pseudo-contractions by using a hybrid projection algorithm in Banach spaces …