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In this work, we present a new class of equilibrium problems, termed as triequilibrium-like problems with trifunction in invexity settings. Classical varilunational-like inequalities and equilibrium-like problems can be obtained as specific variants of triequilibrium-like problems. Certain new iterative methods are proposed and examined for the solution of triequilibrium-like problems by using auxiliary principle technique. Convergence analysis of these proposed methods is examined under some mild conditions.