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1
Content available remote

Some locally mean ergodic theorems

100%
Tam P., Tan K.-K.
Studia Mathematica
|
2002
|
tom 152
|
nr 1
1-9
EN
The notion of local mean ergodicity is introduced. Some general locally mean ergodic theorems for linear and affine operators are presented. Locally mean ergodic theorems for affine operators whose linear parts are compact or similar to subnormal operators on a Hilbert space are given.
2
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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

100%
Chowdhury M., Tan K.-K.
Open Mathematics
|
2010
|
tom 8
|
nr 1
158-169
EN
In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
3
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A minimax inequality with applications to existence of equilibrium point and fixed point theorems

100%
Ding X. P., Tan K.-K.
Colloquium Mathematicum
|
1992
|
tom 63
|
nr 2
233-247
EN
Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an equilibrium point in a one-person game. Next, by applying the minimax inequality, we present some fixed point theorems for set-valued inward and outward mappings on a non-compact convex set in a topological vector space. These results generalize the corresponding results due to Browder [5], Jiang [11] and Shih Tan [15] in several aspects.
4
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Generalized variational-like inequalities for pseudo-monotone type III operators

100%
Chowdhury M., Tan K.-K.
Open Mathematics
|
2008
|
tom 6
|
nr 4
526-536
EN
Our aim in this paper is mainly to prove some existence results for solutions of generalized variational-like inequalities with (η,h)-pseudo-monotone type III operators defined on non-compact sets in topological vector spaces.
5
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A perturbation characterization of compactness of self-adjoint operators

81%
Radjavi H., Tam P.-K., Tan K.-K.
Studia Mathematica
|
2003
|
tom 158
|
nr 3
199-205
EN
A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.
6
Content available remote

Mean ergodicity for compact operators

81%
Radjavi H., Tam P.-K., Tan K.-K.
Studia Mathematica
|
2003
|
tom 158
|
nr 3
207-217
EN
A mean ergodic theorem is proved for a compact operator on a Banach space without assuming mean-boundedness. Some related results are also presented.
7
Content available remote

Quasi-nonexpansive multi-valued maps and selections

80%
Shiau C., Tan K.-K., Wong C. S.
Fundamenta Mathematicae
|
1975
|
tom 87
|
nr 2
109-119
8
Content available remote

A further generalization of Ky Fan's maximal inequality and its applications

80%
Shih M.-H., Tan K.-K.
Studia Mathematica
|
1984
|
tom 78
|
nr 3
279-287
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