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The result improved the corresponding results of Moudafi [15] and Xu [16].
His result improved the corresponding results of Dutta and Choudhury [11] and Dorić [10].
Zhang et al. [17] established some minimax theorems for two set-valued mappings, which improved the corresponding results in [12, 13].
By using a special way of choosing the indices of involved mappings, Deng [14] recently improved the corresponding results announced by Zhang et al. [13].
Their results extended and improved the corresponding ones announced by Nakajo and Takahashi [9], Martinez-Yanes and Xu [12], and Matsushita and Takahashi [4].
Remark 2.1 Our result in Theorem 2.3 improved the corresponding result in [10] (Theorem 3.4) and removed some restriction conditions: the successive sequences have convergent subsequences.
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Post-aluminizing was performed on the sputtered coating to improve the corresponding high-temperature properties.
It emphasizes the need for conversion of the heaviest feeds and for improving the corresponding refining catalysts.
The obtained results can be used to improve the characteristics of work vehicles, in order to reduce the corresponding adverse effects and, consequently, improve the corresponding working conditions.
The main results mainly improve the corresponding results in [11 15].
Also our result improves the corresponding results in [4].
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