Common Fixed Point Theorems in a Complete 2-metric Space

Debashis Dey; Mantu Saha

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 1, page 79-87
  • ISSN: 0231-9721

Abstract

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In the present paper, we establish a common fixed point theorem for four self-mappings of a complete 2-metric space using the weak commutativity condition and A -contraction type condition and then extend the theorem for a class of mappings.

How to cite

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Dey, Debashis, and Saha, Mantu. "Common Fixed Point Theorems in a Complete 2-metric Space." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.1 (2013): 79-87. <http://eudml.org/doc/260733>.

@article{Dey2013,
abstract = {In the present paper, we establish a common fixed point theorem for four self-mappings of a complete 2-metric space using the weak commutativity condition and $A$-contraction type condition and then extend the theorem for a class of mappings.},
author = {Dey, Debashis, Saha, Mantu},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {fixed point; common fixed point; 2-metric space; completeness; fixed point; common fixed point; 2-metric space; completeness},
language = {eng},
number = {1},
pages = {79-87},
publisher = {Palacký University Olomouc},
title = {Common Fixed Point Theorems in a Complete 2-metric Space},
url = {http://eudml.org/doc/260733},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Dey, Debashis
AU - Saha, Mantu
TI - Common Fixed Point Theorems in a Complete 2-metric Space
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 1
SP - 79
EP - 87
AB - In the present paper, we establish a common fixed point theorem for four self-mappings of a complete 2-metric space using the weak commutativity condition and $A$-contraction type condition and then extend the theorem for a class of mappings.
LA - eng
KW - fixed point; common fixed point; 2-metric space; completeness; fixed point; common fixed point; 2-metric space; completeness
UR - http://eudml.org/doc/260733
ER -

References

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  1. Akram, M., Zafar, A. A., Siddiqui A. A., A general class of contractions: A -contractions, Novi Sad J. Math. 38, 1 (2008), 25–33. (2008) Zbl1274.54092MR2498688
  2. Bianchini, R., Su un problema di S.Reich riguardante la teori dei punti fissi, Boll. Un. Math. Ital. 5 (1972), 103–108. (1972) MR0308875
  3. Cho, Y. J., Khan, M. S., Singh, S. L., Common fixed points of weakly commuting mappings, Univ. u Novom Sadu, Zb. Rad. Prirod.–Mat. Fak. Ser. Mat. 18, 1 (1988), 129–142. (1988) Zbl0708.54037MR1034710
  4. Delbosco, D., An unified approach for the contractive mappings, Jnanabha 16 (1986), 1–11. (1986) MR0882131
  5. Fisher, B., Common fixed points of four mappings, Bull. Inst. Math. Acad. Sinicia 11 (1983), 103–113. (1983) Zbl0515.54029MR0718906
  6. Gähler, S., 10.1002/mana.19630260109, Math.Nachr. 26 (1963), 115–148. (1963) MR0162224DOI10.1002/mana.19630260109
  7. Gähler, S, 10.1002/mana.19640280309, Math. Nachr. 28 (1965), 235–244. (1965) DOI10.1002/mana.19640280309
  8. Kannan, R., 10.2307/2316437, Amer. Math. Monthly 76, 4 (1969), 405–408. (1969) Zbl0179.28203MR0257838DOI10.2307/2316437
  9. Khan, M. D., A Study of Fixed Point Theorems, Doctoral Thesis, Aligarh Muslim University, Aligarh, Uttar Pradesh, India, 1984. (1984) 
  10. Naidu, S. V. R., Prasad, J. R., Fixed points in 2- metric spaces, Indian J. Pure AppL. Math. 1, 8 (1986), 974–993. (1986) 
  11. Reich, S., Kannan’s fixed point theorem, Boll. Un. Math. Ital. 4 (1971), 1–11. (1971) Zbl0219.54042MR0305163

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