Some results on pre-monotone operators

Authors

  • M. Roohi Department of Mathematics‎, ‎Faculty of Sciences‎, ‎Golestan University‎, ‎P.O‎. ‎Box ‎155‎, ‎Gorgan‎, ‎Iran.
  • M.H. Alizadeh Department of Mathematics‎, ‎Institute for Advanced Studies in Basic Sciences (IASBS)‎, ‎Zanjan‎, ‎Iran‎.
Abstract:

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is investigated‎. ‎Moreover‎, ‎some results on the sum and difference of two $sigma$-monotone operators is considered.

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Journal title

volume 43  issue 6

pages  2085- 2097

publication date 2017-11-30

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