IJPAM: Volume 96, No. 4 (2014)

SOME COMMON FIXED POINT THEOREMS FOR THREE
PAIRS OF MAPPINGS VIA WEAKLY COMMUTING AND
WEAKLY COMPATIBILITY IN $G$-METRIC SPACES

Surjeet Singh Tomar$^1$, Deepak Singh$^2$, P.C. Dixit$^3$, M.S. Rathore$^4$
$^1$Jai Narayan College of Technology
Bhopal, M.P., INDIA
$^2$Department of Applied Sciences
NITTTR, Under Ministry of HRD
Govt. of India, Bhopal, (M.P.), 462002, INDIA
$^3$Department of Mathematics
T.I.T. College, Bhopal, INDIA
$^4$Department of Mathematics
Chandrashekhar Azad Govt. P.G. College
Sehore, M.P., INDIA


Abstract. The purpose of this paper is to establish the existance and uniqueness of fixed point theorems for three pairs of self mappings in the frame work of complete $G$-metric spaces. Our results are obtained by using the contractive conditions weakly commuting for one pair and weakly compatibility for other two pairs. These results generalize and partially extend some recent results in existing literature.

Received: November 10, 2013

AMS Subject Classification: 47H10, 54H25

Key Words and Phrases: complete $G$-metric space, weakly commuting mappings, weakly compatible mappings, contractive conditions

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DOI: 10.12732/ijpam.v96i4.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 96
Issue: 4
Pages: 427 - 444


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