Complex Anal. Oper. Theory DOI 10.1007/s11785-013-0296-4 Complex Analysis and Operator Theory Bicomplex Analogue of Zalcman Lemma K. S. Charak · N. Sharma Received: 18 June 2012 / Accepted: 18 March 2013 © Springer Basel 2013 Abstract In this paper a bicomplex analogue of Zalcman’s heuristic principle on nor- mal families of meromorphic functions is obtained and as an application a bicomplex version of Lappan’s five-point theorem is proved. Keywords Bicomplex numbers · Normal families · Bicomplex holomorphic functions · Bicomplex meromorphic functions · Bicomplex Riemann sphere Mathematics Subject Classification (2000) 30G · 30D30 · 30G35 · 32A · 32A30 1 Introduction The study of normal families of bicomplex meromorphic functions is initiated in [2] and [3]. The ultimate purpose of this study is to look into the dynamics of bicomplex meromorphic functions. However, the normality of the families of such functions is very interesting in its own right. One natural way to continue is to see whether the results from one variable theory-normal families of meromorphic functions on plane domains-hold for families of bicomplex meromorphic functions since differences do occur in most of the situations. In this direction, we have obtained a bicomplex analogue of Zalcman’s heuristic principle(cf. [7]) and as an application a bicomplex version of Lappan’s five-point theorem [4] is proved. Communicated by Michael Shapiro. K. S. Charak (B) · N. Sharma Department of Mathematics, University of Jammu, 180 006 Jammu, India e-mail: kscharak7@rediffmail.com N. Sharma e-mail: narinder25sharma@sify.com