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Kanokwan?Wongchan Satit?SaejungEmail authorView authors OrcID profile 《Positivity》2018,22(4):969-982
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Satit Saejung 《Journal of Mathematical Analysis and Applications》2008,337(1):123-129
We present some sufficient conditions for normal structure of Banach spaces and their dual spaces in terms of the characteristic of convexity, the James constant, and the coefficient of weak orthogonality. Many known results are improved and strengthened. We also show that some of our results are sharp. 相似文献
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Satit Saejung 《Journal of Global Optimization》2013,56(1):121-129
The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115–125, 2006) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226–240, 2000) and to give a supplement to these results. With the new technique proposed by Maingé (Comput Math Appl 59(1):74–79, 2010), we show that the convergence of the iterative scheme is established under another assumption. It is noted that if the computation error is zero or the approximate computation is exact, our new result is a genuine generalization of Xu’s result and Kamimura–Takahashi’s result. 相似文献
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We characterize the extreme points and smooth points of the unit ball of certain direct sums of Banach spaces. We use these results to characterize noncreasiness and uniform noncreasiness of direct sums, thereby extending results of the second author [S. Saejung, Extreme points, smooth points and noncreasiness of ψ-direct sum of Banach spaces, Nonlinear Anal. 67 (2007) 1649–1653]. 相似文献
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We present two sufficient conditions for normal structure in a Banach space. The first one is given in terms of the new modulus which is a generalization of Gao’s modulus of U-convexity and the second one is given by the presence of full 2-rotundity of the dual space and the WORTH property. 相似文献
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Based on the convergence theorem recently proved by the second author, we modify the iterative scheme studied by Moudafi for quasi-nonexpansive operators to obtain strong convergence to a solution of the split common fixed point problem. It is noted that Moudafi's original scheme can conclude only weak convergence. As a consequence, we obtain strong convergence theorems for split variational inequality problems for Lipschitz continuous and monotone operators, split common null point problems for maximal monotone operators, and Moudafi's split feasibility problem. 相似文献
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We use Mann’s iteration and the hybrid method in mathematical programming to obtain weak and strong convergence to common fixed points of a countable family of Lipschitzian mappings. Finally, we apply our results to solve the equilibrium problems and variational inequalities for continuous monotone mappings. 相似文献
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Weak and strong convergence theorems of an implicit iteration for a countable family of continuous pseudocontractive mappings 总被引:1,自引:0,他引:1
Daruni Boonchari Satit Saejung 《Journal of Computational and Applied Mathematics》2009,233(4):1108-1116
To approximate a common fixed point of a countable family of continuous pseudocontractive mappings, we introduce an implicit iteration sequence. A necessary and sufficient condition for the convergence of a sequence of such iterates for countably many continuous pseudocontractive mappings is given. We also prove the convergence theorems of an implicit iteration sequence for a countable family of strictly pseudocontractive mappings. 相似文献
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On James and von Neumann-Jordan constants and sufficient conditions for the fixed point property 总被引:1,自引:0,他引:1
Satit Saejung 《Journal of Mathematical Analysis and Applications》2006,323(2):1018-1024
In this paper, we prove that a Banach space X and its dual space X∗ have uniform normal structure if . The García-Falset coefficient R(X) is estimated by the CNJ(X)-constant and the weak orthogonality coefficient introduced by B. Sims. Finally, we present an affirmative answer to a conjecture by L. Maligranda concerning the relation between the James and CNJ(X)-constants for a Banach space. 相似文献