# Some results on pre-monotone operators

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Institute for Advanced Studies in Basic Sciences (IASBS)‎, ‎Zanjan‎, ‎Iran‎.

2 Department of Mathematics‎, ‎Faculty of Sciences‎, ‎Golestan University‎, ‎P.O‎. ‎Box ‎155‎, ‎Gorgan‎, ‎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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Main Subjects

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### History

• Receive Date: 15 February 2016
• Revise Date: 28 December 2016
• Accept Date: 29 December 2016