Abstract
Using the KKM mapping technique, we obtain existence results for the mixed equilibrium problem (under the relaxed \(\alpha \)-monotonicity assumption on the bi-function) in a reflexive Banach space. Several examples are given to show that our definition of \(\alpha \)-monotonicity and, hence, our results are more general than that in the existing literature.
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Acknowledgments
We are grateful to the editor and anonymous reviewers for their constructive comments and valuable suggestions. The work of the authors was partially supported by CSIR, New Delhi, grant 25(0163)/08/EMR-II.
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Mahato, N.K., Nahak, C. Mixed equilibrium problems with relaxed \(\alpha \)-monotone mapping in Banach spaces. Rend. Circ. Mat. Palermo 62, 207–213 (2013). https://doi.org/10.1007/s12215-013-0103-0
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DOI: https://doi.org/10.1007/s12215-013-0103-0