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Some new common fixed point theorems in fuzzy metric spaces

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Abstract

The purpose of this paper is to prove some new common fixed point theorems in (GV)-fuzzy metric spaces. While proving our results, we utilize the idea of compatibility due to Jungck (Int J Math Math Sci 9:771–779, 1986) together with subsequentially continuity due to Bouhadjera and Godet-Thobie (arXiv: 0906.3159v1 [math.FA] 17 Jun 2009) respectively (also alternately reciprocal continuity due to Pant (Bull Calcutta Math Soc 90:281–286, 1998) together with subcompatibility due to Bouhadjera and Godet-Thobie (arXiv:0906.3159v1 [math.FA] 17 Jun 2009) as patterned in Imdad et al. (doi:10.1016/j.aml.2011.01.045) wherein conditions on completeness (or closedness) of the underlying space (or subspaces) together with conditions on continuity in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant results due to Imdad et al. (J Appl Math Inform 26:591–603, 2008), Mihet (doi:10.1016/j.na.2010.05.044), Mishra (Tamkang J Math 39(4):309–316, 2008), Singh (Fuzzy Sets Syst 115:471–475, 2000) and several others.

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Authors and Affiliations

  1. Department of Applied Mathematics and Humanities, S. V. National Institute of Technology, Surat, 395007, Gujarat, India

    D. Gopal

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    M. Imdad

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  1. D. Gopal
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  2. M. Imdad
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Correspondence to D. Gopal.

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Gopal, D., Imdad, M. Some new common fixed point theorems in fuzzy metric spaces. Ann Univ Ferrara 57, 303–316 (2011). https://doi.org/10.1007/s11565-011-0126-4

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  • DOI: https://doi.org/10.1007/s11565-011-0126-4

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