, Volume 51, Issue 2, pp 257–269 | Cite as

Equilibrium problems with generalized relaxed monotonicities in Banach spaces

  • Nihar Kumar Mahato
  • Chandal NahakEmail author
Theoretical Article


In this paper, we introduce the concepts of generalized relaxed α-monotonicity and generalized relaxed α-pseudomonotonicity for bi-functions. By using the KKM technique, we obtain existence solution of the mixed equilibrium problems with the generalized relaxed α-monotonicity in reflexive Banach spaces. We also, obtain the existence results for classical equilibrium problem with the generalized relaxed α-pseudomonotonicity.


Equilibrium problem Mixed equilibrium problem Generalized relaxed α-monotonicity Generalized relaxed α-pseudomonotonicity KKM mappings 

Mathematics Subject Classification (2010)

47H04 47H05 90C33 


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Copyright information

© Operational Research Society of India 2013

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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