SOLVABILITY OF GENERALIZED MIXED MONOTONE OPERATOR EQUATIONS IN PARTIALLY ORDERED SPACES AND APPLICATIONS

LUO Ting, ZHU Chuanxi

Journal of Systems Science and Mathematical Sciences ›› 2014, Vol. 34 ›› Issue (5) : 589-601.

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PDF(314 KB)
Journal of Systems Science and Mathematical Sciences ›› 2014, Vol. 34 ›› Issue (5) : 589-601. DOI: 10.12341/jssms12326

SOLVABILITY OF GENERALIZED MIXED MONOTONE OPERATOR EQUATIONS IN PARTIALLY ORDERED SPACES AND APPLICATIONS

  • LUO Ting, ZHU Chuanxi
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Abstract

In this paper, the new concepts of generalized mixed monotone operators N:X×X×XX and tripled quasi-solutions for operator equations Lx=N(x,y,z) are introduced.By using partial order method and cone theory, the existence of tripled quasi-solutions for generalized mixed monotone operator equations Lx=N(x,y,z) under the condition of  forward and counter upper-down solutions are studied in complete  metric spaces and Banach spaces. Then the existence of solutions for   generalized mixed monotone operator equations Lx=N(x,x,x) is studied in Banach spaces. The results extend and improve some  existing  results. Finally, an example is given to illustrate  the validity of the main results.

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LUO Ting, ZHU Chuanxi. SOLVABILITY OF GENERALIZED MIXED MONOTONE OPERATOR EQUATIONS IN PARTIALLY ORDERED SPACES AND APPLICATIONS. Journal of Systems Science and Mathematical Sciences, 2014, 34(5): 589-601 https://doi.org/10.12341/jssms12326
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