View More View Less
  • 1 Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur 208 016, India
  • | 2 Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
  • | 3 Faculty of Mathematics and Computer Science, West University of Timisoara, Bv. V. Parvan 4, 300223 Timisoara, Romania
  • | 4 School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi 110 067, India
Restricted access

Abstract

The aim of this paper is to prove some common fixed point theorems 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] Aamri, A., Moutawakil El, D. 2002 Some new common fixed point theorems under strict contractive conditions J. Math. Anal. Appl. 270 181188 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2] Naschie El, M. S. 2007 A review of applications and results of E-infinity theory Int. J. Nonlinear Sci. Numer. Simul. 8 1120 .

  • [3] Fang, J.-X., Gao, Y. 2009 Common fixed point theorems under strict contractive conditions in Menger spaces Nonlinear Anal. 70 184193 .

  • [4] Hadzić, O., Pap, E. 2001 Fixed Point Theory in Probabilistic Metric Spaces Kluwer Academic Publishers Dordrecht.

  • [5] Imdad, M., Ali, Javid, Khan, L. 2006 Coincidence and fixed points in symmetric spaces under strict contractions J. Math. Anal. Appl. 320 352360 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [6] Imdad, M., Ali, Javid 2008 Jungck’s common fixed point theorem and E.A property Acta Math. Sinica 24 8794 .

  • [7] Imdad, M., Ali, Javid, Tanveer, M. 2009 Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces Chaos, Solitons & Fractals 42 31213129 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [8] Jungck, G. 1986 Compatible mappings and common fixed points Internat. J. Math. Math. Sci. 9 771779 .

  • [9] Jungck, G. 1988 Common fixed point for commuting and compatible maps on compacta Proc. Amer. Math. Soc. 103 977983 .

  • [10] Jungck, G. 1996 Common fixed points for non continuous non self maps on non metric spaces Far East J. Math. Sci. 4 199215.

  • [11] Kasahara, S., Rhoades, B. E. 1978 Common fixed point theorems in compact metric spaces Math. Japon. 23 227229.

  • [12] Kubiaczyk, I., Sharma, S. 2008 Some common fixed point theorems in Menger space under strict contractive conditions Southeast Asian Bull. Math. 32 117124.

    • Search Google Scholar
    • Export Citation
  • [13] Liu, Y., Wu, Jun, Li, Z. 2005 Common fixed points of single-valued and multi-valued maps Internat. J. Math. Math. Sci. 19 30453055 .

  • [14] Menger, K. 1942 Statistical metrics Proc. Nat. Acad. Sci. USA 28 535537 .

  • [15] Menger, K. 1951 Probabilistic geometry Proc. Nat. Acad. Sci. USA 37 226229 .

  • [16] Mihet, D. 2009 A note on a common fixed point theorem in probabilistic metric spaces Acta Math. Hungar. 125 127130 .

  • [17] Mihet, D. 2010 Fixed point theorems in fuzzy metric spaces using property E.A Nonlinear Anal. 73 21842188 .

  • [18] Mihet, D. 2005 A generalization of a contraction principle in probabilistic metric spaces, II Internat. J. Math. Math. Sci. 5 729736 .

  • [19] Mishra, S. N. 1991 Common fixed points of compatible mappings in PM-spaces Math. Japon. 36 283289.

  • [20] Pant, R. P. 1994 Common fixed points of non commuting mappings J. Math. Anal. Appl. 188 436440 .

  • [21] Pant, R. P. 1998 Common fixed points of contractive maps J. Math. Anal. Appl. 226 251258 .

  • [22] Pant, R. P. 1999 R-weak commutativity and common fixed points Soochow J. Math. 25 3742.

  • [23] Pant, R. P., Pant, V. 2000 Common fixed point under strict contractive conditions J. Math. Anal. Appl. 248 327332 .

  • [24] Razani, A., Shirdaryazdi, M. 2007 A common fixed point theorem of compatible maps in Menger space Chaos, Solitons & Fractals 32 2634 .

  • [25] Schweizer, B., Sklar, A. 1983 Probabilistic Metric Spaces Elsevier, North Holland New York.

  • [26] Sehgal, V. M., Bharucha-Reid, A. T. 1972 Fixed point of contraction mappings on probabilistic metric spaces Math. Systems Theory 6 97102 .

  • [27] Singh, B., Jain, S. 2005 A fixed point theorem in Menger space through weak compatibility J. Math. Anal. Appl. 301 439448 .

Acta Mathematica Hungarica
P.O. Box 127
HU–1364 Budapest
Phone: (36 1) 483 8305
Fax: (36 1) 483 8333
E-mail: acta@renyi.mta.hu

  • Impact Factor (2019): 0.588
  • Scimago Journal Rank (2019): 0.489
  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

For subscription options, please visit the website of Springer Nature

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)