An iterative process for nonlinear lipschitzian and strongly accretive mappings in uniformly convex and uniformly smooth Banach spaces

1993 ◽  
Vol 32 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Lei Deng
Keyword(s):  
Banach Spaces ◽  
Iterative Process ◽  
Uniformly Convex ◽  
Uniformly Smooth ◽  
Accretive Mappings ◽  
Uniformly Smooth Banach Spaces

scholarly journals Inertial Krasnoselskii–Mann Method in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 638
Author(s):  
Yekini Shehu ◽  
Aviv Gibali
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Splitting Method ◽  
Uniformly Convex ◽  
Inclusion Problems ◽  
Uniformly Smooth ◽  
Mann Algorithm ◽  
Uniformly Smooth Banach Spaces

In this paper, we give a general inertial Krasnoselskii–Mann algorithm for solving inclusion problems in Banach Spaces. First, we establish a weak convergence in real uniformly convex and q-uniformly smooth Banach spaces for finding fixed points of nonexpansive mappings. Then, a strong convergence is obtained for the inertial generalized forward-backward splitting method for the inclusion. Our results extend many recent and related results obtained in real Hilbert spaces.

scholarly journals Generalized Projections on Closed Nonconvex Sets in Uniformly Convex and Uniformly Smooth Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convex Set ◽  
Variational Problems ◽  
Generalized Projection ◽  
Uniformly Convex ◽  
Uniformly Smooth ◽  
Nonconvex Sets ◽  
Generalized Projections ◽  
Uniformly Smooth Banach Spaces

The present paper is devoted to the study of the generalized projectionπK:X∗→K, whereXis a uniformly convex and uniformly smooth Banach space andKis a nonempty closed (not necessarily convex) set inX. Our main result is the density of the pointsx∗∈X∗having unique generalized projection over nonempty close sets inX. Some minimisation principles are also established. An application to variational problems with nonconvex sets is presented.

scholarly journals Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces

2016 ◽  
Vol 25 (1) ◽  
pp. 107-120
Author(s):  
T. M. M. SOW ◽  
◽  
C. DIOP ◽  
N. DJITTE ◽  
◽  
...  
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Real Banach Space ◽  
Monotone Mappings ◽  
Uniformly Convex ◽  
Hammerstein Equation ◽  
Uniformly Smooth ◽  
Monotone Maps

For q > 1 and p > 1, let E be a 2-uniformly convex and q-uniformly smooth or p- uniformly convex and 2-uniformly smooth real Banach space and F : E → E∗, K : E∗ → E be bounded and strongly monotone maps with D(K) = R(F) = E∗. We construct a coupled iterative process and prove its strong convergence to a solution of the Hammerstein equation u + KF u = 0. Futhermore, our technique of proof is of independent of interest.

scholarly journals A New Hybrid Algorithm forλ-Strict Asymptotically Pseudocontractions in 2-Uniformly Smooth Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Xin-dong Liu ◽  
Shih-sen Chang
Keyword(s):  
Banach Spaces ◽  
Hybrid Algorithm ◽  
Metric Projection ◽  
Projection Algorithm ◽  
Strong Convergence Theorem ◽  
Uniformly Convex ◽  
Uniformly Smooth ◽  
Hybrid Projection Algorithm ◽  
Uniformly Smooth Banach Spaces ◽  
Asymptotically Pseudocontractive Mapping

A new hybrid projection algorithm is considered for aλ-strict asymptotically pseudocontractive mapping. Using the metric projection, a strong convergence theorem is obtained in a uniformly convex and 2-uniformly smooth Banach spaces. The result presented in this paper mainly improves and extends the corresponding results of Matsushita and Takahashi (2008), Dehghan (2011) Kang and Wang (2011), and many others.

Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces

2016 ◽  
Vol 25 (1) ◽  
pp. 107-120
Author(s):  
T. M. M. SOW ◽  
◽  
C. DIOP ◽  
N. DJITTE ◽  
◽  
...  
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Real Banach Space ◽  
Monotone Mappings ◽  
Uniformly Convex ◽  
Hammerstein Equation ◽  
Uniformly Smooth ◽  
Monotone Maps

For q > 1 and p > 1, let E be a 2-uniformly convex and q-uniformly smooth or p- uniformly convex and 2-uniformly smooth real Banach space and F : E → E∗, K : E∗ → E be bounded and strongly monotone maps with D(K) = R(F) = E∗. We construct a coupled iterative process and prove its strong convergence to a solution of the Hammerstein equation u + KF u = 0. Futhermore, our technique of proof is of independent of interest.

A CONVERGENCE THEOREM FOR COMMON ELEMENTS OF EQUILIBRIUM PROBLEMS AND MAPPINGS SATISFYING CONDITION (Φ-Eµ) IN UNIFORMLY CONVEX AND UNIFORMLY SMOOTH BANACH SPACES

2018 ◽  
Vol 1 (30) ◽  
pp. 67-77
Author(s):  
Hieu Trung Nguyen ◽  
Tien Cam Truong
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Satisfying Condition ◽  
Common Element ◽  
Uniformly Convex ◽  
Fixed Point Set ◽  
Uniformly Smooth ◽  
Point Set ◽  
Uniformly Smooth Banach Spaces

In this paper, we propose a new hybrid iteration for finding a common element of solution set of equilibrium problems and the fixed point set of mappings  satisfying condi- tion (Φ-Eµ), and establish the convergence of this iteration in uniformly convex and uniformly smooth Banach spaces. From this theorem, we geta corollary for the convergence for equilibrium problems and mappings satisfying condition (Eµ) in real Hilbert spaces. In addition, an example is provided to illustrate for the convergence of equilibrium problems and mappings satisfying condition (Φ-Eµ). These results are the generations and improvements of some  existing results in the literature

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