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Dive into the research topics where Satit Saejung is active.

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Featured researches published by Satit Saejung.


Fixed Point Theory and Applications | 2008

Strong Convergence to Common Fixed Points of Countable Relatively Quasi-Nonexpansive Mappings

Weerayuth Nilsrakoo; Satit Saejung

Correspondence should be addressed to Satit Saejung,[email protected] 30 August 2007; Accepted 24 December 2007Recommended by Simeon ReichWe prove that a sequence generated by the monotone CQ-method converges strongly to a commonfixed point of a countable family of relatively quasi-nonexpansive mappings in a uniformly convexand uniformly smooth Banach space. Our result is applicable to a wide class of mappings.Copyrightq2008 W. Nilsrakoo and S. Saejung. This is an open access article distributed underthe Creative Commons Attribution License, which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.


Fixed Point Theory and Applications | 2010

Halpern's Iteration in CAT(0) Spaces

Satit Saejung

Motivated by Halperns result, we prove strong convergence theorem of an iterative sequence in CAT(0) spaces. We apply our result to find a common fixed point of a family of nonexpansive mappings. A convergence theorem for nonself mappings is also discussed.


Applied Mathematics and Computation | 2011

Strong convergence theorems by Halpern–Mann iterations for relatively nonexpansive mappings in Banach spaces

Weerayuth Nilsrakoo; Satit Saejung

Abstract In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.


Proceedings of the American Mathematical Society | 2005

The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces

Antonio Jiménez-Melado; Enrique Llorens-Fuster; Satit Saejung

We give some sufficient conditions for normal structure in terms of the von Neumann-Jordan constant, the James constant and the weak orthogonality coefficient introduced by B. Sims. In the rest of the paper, the von Neumann-Jordan constant and the James constant for the Bynum space l 2,∞ are computed, and are used to show that our results are sharp.


Applied Mathematics and Computation | 2006

A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings

Weerayuth Nilsrakoo; Satit Saejung

In the present paper, we define and study a new three-step iterative scheme inspired by Suantai [J. Math. Anal. Appl. 311 (2005) 506-517]. This scheme includes many well-known iterations, for examples, modified Mann-type, modified Ishikawa-type iterative schemes, and the three-step iterative scheme of Xu and Noor. Several convergence theorems of this scheme are established for asymptotically nonexpansive mappings. Our results extend and improve the recent ones announced by Schu [J. Math. Anal. Appl. 158 (1991) 407-413; Bull. Aust. Math. Soc. 43 (1991) 153-159], Xu and Noor [J. Math. Anal. Appl. 267 (2002) 444-453], Suantai [J. Math. Anal. Appl. 311 (2005) 506-517], and many others. A misleading conclusion of Theorem 2.6 in Suantais paper is also corrected.


Applied Mathematics and Computation | 2010

Construction of common fixed points of a countable family of λ-demicontractive mappings in arbitrary Banach spaces

Daruni Boonchari; Satit Saejung

We propose iterative Mann-type schemes to approximate a common fixed point of a countable family of @l-demicontractive and L-Lipschitzain mappings. This improves the recent result of Chidume et al. [C.E. Chidume, M. Abbas, Bashir Ali, Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings. Appl. Math. Comput. 194(1) (2007) 1-6] from a single strictly pseudocontractive mapping to a family of more general mappings.


Journal of Optimization Theory and Applications | 2014

Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces

Rapeepan Kraikaew; Satit Saejung

Building upon the subgradient extragradient method proposed by Censor et al., we prove the strong convergence of the iterative sequence generated by a modification of this method by means of the Halpern method. We also consider the problem of finding a common element of the solution set of a variational inequality and the fixed-point set of a quasi-nonexpansive mapping with a demiclosedness property.


Fixed Point Theory and Applications | 2008

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Satit Saejung

We prove a convergence theorem by the new iterative method introduced by Takahashi et al. (2007). Our result does not use Bochner integrals so it is different from that by Takahashi et al. We also correct the strong convergence theorem recently proved by He and Chen (2007).


Fixed Point Theory and Applications | 2012

Some fixed point theorems in complex valued metric spaces

Kittipong Sitthikul; Satit Saejung

Owning the concept of complex valued metric spaces introduced by Azam et al., we prove several fixed point theorems for mappings satisfying certain point-dependent contractive conditions. The main results announced by Sintunavarat and Kumam (J. Inequal. Appl. 2012:84, 2012), Rouzkard and Imdad (Comput. Math. Appl., 2012, doi:10.1016/j.camwa.2012.02.063), and Dass and Gupta (Indian J. Pure Appl. Math. 6(12):1455-1458, 1975) are deduced from our results under weaker assumptions.


Journal of Computational and Applied Mathematics | 2009

Weak and strong convergence theorems of an implicit iteration for a countable family of continuous pseudocontractive mappings

Daruni Boonchari; Satit Saejung

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.

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Ji Gao

Community College of Philadelphia

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