Acta Math. Hungar., 132 (4) (2011), 367–386 DOI: 10.1007/s10474-011-0105-3 First published online May 20, 2011 COMMON FIXED POINTS OF STRICT CONTRACTIONS IN MENGER SPACES J. ALI 1 , M. IMDAD 2,* , D. MIHET 3 and M. TANVEER 4 1 Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur 208 016, India e-mail: javid@math.com 2 Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India e-mail: mhimdad@yahoo.co.in 3 West University of Timisoara, Faculty of Mathematics and Computer Science, Bv. V. Parvan 4, 300223 Timisoara, Romania e-mail: mihet@math.uvt.ro 4 School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi 110 067, India e-mail: tanveer gouri@yahoo.co.in (Received August 6, 2010; revised January 3, 2011; accepted January 10, 2011) Abstract. The aim of this paper is to prove some common fixed point theo- rems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples. 1. Introduction and preliminaries The concept of probabilistic metric space was initiated and studied by Menger [14,15] which is indeed a statistical generalization of the classical metric space notion. Though the studies of such spaces were pursued by many researchers, yet this study has gained the much needed impetus with the pioneering work of Schweizer and Sklar [25]. The theory of probabilistic metric space is of paramount importance in probabilistic functional analy- sis. Towards the application side, one may recall El Naschie [2] wherein he gave applications of this concept in quantum particle physics particularly in connection with both string and ε ∞ theory. * Corresponding author. Key words and phrases: Menger space, common property (E.A), weakly compatible mapping and t-norm. 2000 Mathematics Subject Classification: primary 47H10, secondary 54H25. 0236-5294/$ 20.00 c  2011 Akad´ emiai Kiad´o, Budapest, Hungary