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The present paper is concerned with the new concept of relaxed α-β-η-monotonicity and relaxed α-βη-pseudomonotonicity in Banach space which is applied to prove the existence of solutions of generalized equilibrium problem and classic equilibrium problem. In this regard, we use the well-known KKM-theory to obtain solutions of mentioned problems.doi:10.22436/jnsa.009.10.16 fatcat:pesmbpzvifd5rgdnqiucjacgfi