Error Bounds for Approximate Solutions of Abstract Inequality Systems and Infinite Systems of Inequalities on Banach Spaces

2020 ◽  
Author(s):  
Jinhua Wang ◽  
Mingwu Ye ◽  
Sy-Ming Guu ◽  
Chong Li
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Approximate Solutions ◽  
Infinite Systems ◽  
Inequality Systems ◽  
Systems Of Inequalities

Error bounds for convex differentiable inequality systems in Banach spaces

2005 ◽  
Vol 104 (2-3) ◽  
pp. 465-482 ◽  
Author(s):  
Huynh van Ngai ◽  
Michel Théra
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Inequality Systems

scholarly journals General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1288
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Norm Inequalities ◽  
Differentiable Functions ◽  
Fréchet Differentiable ◽  
General Norm

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

scholarly journals Iterative methods for generalized split feasibility problems in Banach spaces

2017 ◽  
Vol 33 (1) ◽  
pp. 09-26
Author(s):  
QAMRUL HASAN ANSARI ◽  
◽  
AISHA REHAN ◽  
◽  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Split Feasibility Problems ◽  
Convergence Results ◽  
Split Feasibility

Inspired by the recent work of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205–221], in this paper, we study generalized split feasibility problems (GSFPs) in the setting of Banach spaces. We propose iterative algorithms to compute the approximate solutions of such problems. The weak convergence of the sequence generated by the proposed algorithms is studied. As applications, we derive some algorithms and convergence results for some problems from nonlinear analysis, namely, split feasibility problems, equilibrium problems, etc. Our results generalize several known results in the literature including the results of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, SetValued Var. Anal., 23 (2015), 205–221].

Nonlinear error bounds for quasiconvex inequality systems

2015 ◽  
Vol 11 (1) ◽  
pp. 107-120 ◽  
Author(s):  
Satoshi Suzuki ◽  
Daishi Kuroiwa
Keyword(s):  
Error Bounds ◽  
Nonlinear Error ◽  
Inequality Systems ◽  
Nonlinear Error Bounds
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