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In this paper, we define weak $\theta_m-$ contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak $\theta_m-$ iterated multifunction system. Moreover, we introduce $(\alpha,\beta,\theta_m)-$ contractions using cyclic $(\alpha,\beta)-$ admissible mappings and obtain some results for such class of mappings without the continuity of the operator. Wedoi:10.4995/agt.2020.11992 fatcat:oymdoxtcfffyppweuzedujjitq