@article { author = {Alizadeh, M.H. and Roohi, M.}, title = {Some results on pre-monotone operators}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {6}, pages = {2085-2097}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, 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.}, keywords = {Generalized monotone operators‎,‎upper semicontinuous‎,‎convex function‎}, url = {http://bims.iranjournals.ir/article_1085.html}, eprint = {http://bims.iranjournals.ir/article_1085_cc4d2b57b686d6c39e4e826525d95114.pdf} }