Abstract
We introduce strong pseudomonotone and strong quasimonotone maps of higher order and establish their relationships with strong pseudoconvexity and strong quasiconvexity of higher order, respectively, which yields first-order characterizations of strong pseudoconvex and strong quasiconvex functions of higher order. Moreover, we answer the open problem (converse part of Proposition 6.2) of Karamardian and Schaible (J. Optim. Theory Appl. 66:37–46,1990), for even more generalized functions, namely strongly pseudoconvex functions of higher order.
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Acknowledgements
The first author is financially supported by CSIR-UGC JRF, New , India, through Reference no.: 1272/(CSIR-UGC NET DEC.2016). The second author is financially supported by UGC-BHU Research Fellowship, through sanction letter no: Ref.No. /Math/Res/Sept.2015/2015-16/918.
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Singh, S.K., Shahi, A., Mishra, S.K. (2018). On Strong Pseudomonotone and Strong Quasimonotone Maps. In: Ghosh, D., Giri, D., Mohapatra, R., Sakurai, K., Savas, E., Som, T. (eds) Mathematics and Computing. ICMC 2018. Springer Proceedings in Mathematics & Statistics, vol 253. Springer, Singapore. https://doi.org/10.1007/978-981-13-2095-8_2
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