On Lipschitz continuity of approximate solutions to set-valued equilibrium problems via nonlinear scalarization

Optimization ◽  
2021 ◽  
pp. 1-23
Author(s):  
Lam Quoc Anh ◽  
Tran Ngoc Tam ◽  
Nguyen Huu Danh
Keyword(s):  
Equilibrium Problems ◽  
Lipschitz Continuity ◽  
Approximate Solutions ◽  
Nonlinear Scalarization

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].

scholarly journals Constrained Weak Nash-Type Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
W. C. Shuai ◽  
K. L. Xiang ◽  
W. Y. Zhang
Keyword(s):  
Existence Theorem ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Existence Results ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalarization Function ◽  
Payoff Functions

A constrained weak Nash-type equilibrium problem with multivalued payoff functions is introduced. By virtue of a nonlinear scalarization function, some existence results are established. The results extend the corresponding one of Fu (2003). In particular, if the payoff functions are singlevalued, our existence theorem extends the main results of Fu (2003) by relaxing the assumption of convexity.

scholarly journals A Third Order Newton-Like Method and Its Applications

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 31 ◽  
Author(s):  
D. Sahu ◽  
Ravi Agarwal ◽  
Vipin Singh
Keyword(s):  
Nonlinear Operator ◽  
Lipschitz Continuity ◽  
Approximate Solutions ◽  
Continuity Condition ◽  
Convergence Theory ◽  
Fredholm Integral Equations ◽  
Third Order ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
First Derivative

In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature.

On the stability of approximate solutions to set-valued equilibrium problems

Optimization ◽  
2019 ◽  
Vol 69 (7-8) ◽  
pp. 1583-1599
Author(s):  
Lam Quoc Anh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Equilibrium Problems ◽  
Approximate Solutions ◽  
The Stability
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