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GENERALIZED SYSTEM FOR RELAXED COCOERCIVE EXTENDED GENERAL VARIATIONAL INEQUALITIES

  • Jun-Min, Chen;Hui, Tong
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.561-567
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    • 2012
  • The approximate solvability of a generalized system for relaxed cocoercive extended general variational inequalities is studied by using the project operator technique. The results presented in this paper are more general and include many previously known results as special cases.

Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

  • Dong, Yongpeng;Fan, Shengjun
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.985-999
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    • 2018
  • This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

ON A CLASS OF LOCALLY PROJECTIVELY FLAT GENERAL (α, β)-METRICS

  • Mo, Xiaohuan;Zhu, Hongmei
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1293-1307
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    • 2017
  • General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.