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(A) IN G-METRIC SPACES 1. Introduction In 1922, Banach

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908 S. Manro, S. Kumar, S. S. Bhatia<br />

[2] C. R. Hsiao, A property of contraction type mappings in 2-metric spaces, Jnanabha<br />

16 (1986), 223–229.<br />

[3] S. Gahler, 2-metrische Raume und ihre topologische Struktur, Math. Nachr. 26 (1963),<br />

115–148.<br />

[4] G. Jungck, Commuting mappings and fixed point, Amer. Math. Monthly 83 (1976),<br />

261–263.<br />

[5] G. Jungck, B. E. Rhoades, Fixed point for set valued functions without continuity,<br />

<strong>In</strong>dian. J. Pure Appl. Math. 29 (1998), 227–238.<br />

[6] Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces, Proceedings of <strong>In</strong>ternational<br />

Conference on Fixed Point Theory and Applications, Yokohama Publishers,<br />

Valencia Spain, July 13–19 (2004), 189–198.<br />

[7] Z. Mustafa, B. Sims, A new approach to a generalized metric spaces, J. Nonlinear<br />

Convex Anal. 7 (2006), 289–297.<br />

[8] Z. Mustafa, H. Obiedat, F. Awawdeh, Some fixed point theorems for mappings on<br />

complete G-metric spaces, Fixed Point Theory Appl., Vol. 2008, Article ID 18970, 12<br />

pages.<br />

[9] Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed points results in G-metric<br />

spaces, <strong>In</strong>ternational Journal of Mathematics and Mathematical Sciences, Vol. 2009,<br />

Article ID 283028, 10 pages.<br />

[10] Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete Gmetric<br />

spaces, Fixed Point Theory and Applications, Vol. 2009, Article ID 917175,<br />

10 pages.<br />

[11] Z. Mustafa, H. Obiedat, A fixed points theorem of Reich in G-metric spaces, Cubo<br />

Math. J. 12 (2010), 83–93.<br />

[12] Z. Mustafa, F. Awawdeh, W. Shatanawi, Fixed point theorem for expansive mappings<br />

in G-metric spaces, <strong>In</strong>t. J. Contemp. Math. Sciences 5 (2010), 2463–2472.<br />

[13] W. Shatanawi, Fixed point theory for contractive mappings satisfying ϕ-maps in Gmetric<br />

spaces, Fixed Point Theory Appl., Vol. 2010, Article ID 181650, 9 pages.<br />

S. Manro, S. S. Bhatia:<br />

SCHOOL OF MATHEMATICS AND COMPUTER<br />

APPLICATIONS, THAPAR UNIVERSITY<br />

PATIALA-147 004, <strong>IN</strong>DIA<br />

E-mail: sauravmanro@yahoo.com<br />

ssbhatia@thapar.edu<br />

S. Kumar:<br />

DEENBANDHU CHHOTU RAM UNIVERSITY OF SCIENCE AND TECHNOLOGY MURTHAL<br />

(SONEPAT), <strong>IN</strong>DIA E-mail: sanjaymudgal2004@yahoo.com<br />

Received August 5, 2010; revised version December 27, 2010.

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