Common fixed point theorems of contractive mappings sequence in partially ordered G-metric spaces

Subject Areas : Applied Mathematics

Leila Gholizadeh ¹ (Department of Mathematics, Science and Research Branch, Islamic Azad University(IAU), Tehran, Iran)

Received: 2013-02-03 Accepted : 2013-10-17 Published : 2015-05-01

Keywords:

Abstract :

We consider the concept of Ω-distance on a complete partially ordered G-metric space and prove some common fixed point theorems.

References:

[1] B. Ahmad, M. Ashraf, B. Rhoades, Fixed point theorem for
expansive mappings in G-metric spaces, J. Pure Appl. Math. 32
(2001) 1513-1518.

[2] R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized in

partially ordered metric space, Appl. Anal. 87(2008) 1-8

[3] M. Abbas, B. Rhoades, Common xed point results for non-
commuting mappings without continuity in generalized metric
spaces,Appl. Math. Comput. 215 (2009) 262-269.
[4] L.B. Ciric, A generalization of Banach's contraction principle, Proc.
Amer. Math. Soc. 45 (1974) 267-273.
[5] L.B. Ciric, Coincidence of xed points for maps on topological
spaces, Topology Appl. 154 (2007) 3100-3106.
[6] L.B. Ciric, S.N. Jsic, M.M. Milovanovic, J.S. Ume, On the steepest
descent approximation method for the zeros of generalized accretive
oprators,Nonlinear Anal-TMA.69 (2008) 763-769.
[7] B.C. Dhoage, Proving xed point theorems in D-metric spaces via
general existence principles,J. Pure Appl. Math. 34 (2003) 609-628.
[8] J.X. Fang, Y. Gao, Common xed point theorems under stric
contractive conditions in Menger space, Nonlinear Anal-TMA. 70
(2006) 184-193.
[9] T. Gnana Bhaskar, V. Lakshmikantham, J. Vasundhara Devi,
Monotone interativ technique for functional dierential equations
with retardation and anticipation, Nonlinear Anal-TMA.66 (2007)
12237-2242.
[10] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in
partially ordered metric spaces and applications, Nonlinear Anal-
TMA. 65 (2006) 1379-1393.
[11] N. Hussain, Common xed point in best approximation for Banach
opaerator pairs with Ciric type I-contractions, J. Math. Anal. Appl.
338 (2008) 1351-1363.
[12] J.J. Nieto, R.R. Lopez, Existence and uniqueness of xed point
in partially ordered sets and applications to ordinary dierential
equations, Acta Math. Sin. Eng. Ser. 23 (2007) 2205-2212.
[13] D. O'Regan, R. Saadati, Nonlinear contraction theorems in
probabilistic spaces, Appl. Math. Comput. 195 (2008) 86-93.
43
[14] E. Firouz, S. J. Hosseini Ghoncheh, Common xed point theorem
for w-distance with new integral type contraction, Mathematics
Scientic Journal. 8 (2013) 33{39.
[15] H. Soleimani, S. M. Vaezpour, M. Asadi, Fixed point theorems and
their stability in metric trees, Mathematics Scientic Journal. 8
(2012) 109{116.
[16] J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems
in partally ordered sets and applications to ordinary dierential
eqquations, order. 22 (2005) 223-239.
[17] A.C.M. Ran, M.C.B. Reurings, A xed point theorem in partially
ordered sets and some applications to matrix equations, Proc. Amer.
Math. Soc. 132 (2004) 1435-1443.
[18] A. Petrusel, L.A. Rus, Fixed point theorems in ordered L-spaces,
Proc. Amer. Math. Soc. 134 (2006) 411-418.
[19] Z. Mustafa, B. Sims, A new approach to generalized metric spaces,
J. Nonlinear Convex Anal. 7 (2006) 289-297.
[20] Z. Mustafa, F. Awawded, W. Shantanawi, Fixed point theorem for
expansive mappings in G-metric spaces, Int. J. Contemp. Math.
Sciences. 5 (2010) 2463-2472.
[21] S. Manro, S.S. Bhatia, S. Kumar, Expansion mappings theorems in
G-metric spaces, J. Contemp. Math. Sciences. 5 (2010) 2529-2535.
[22] Z. Mustafa, T. Obiedat, F. Awawdeh, Some xed point theorems
for mapping on complete G-metric space, Fixed Point theory Appl.
12(2008) Article ID 189870.
[23] Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings
in complete G-metric spaces, Fixed Point theory Appl. 10 (2009)
Article ID 917175.
[24] W. Shatanawi, Fixed point theory for contractive mappings
satisfying -maps in G-metric spaces, Fixed Point theory Appl. 9
(2010) Article ID 181650.
[25] L. Gajic, On a common xed point for sequence of selfmappings in
generalized metric space, J. Math. 36 (2006) 153-156.
44
[26] R. Saadati, S.M. Vaezpour, P. Vetro, B.E. Rhoades, Fixed point
theorems in generalized partially ordered G-metric spaces, Math.
Comput. Model. 52 (2010) 797-801.
[27] O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization
theorems and xed point theorems in complete metric space, Math.
Japonica. 44 (1996) 381-391.
[28] L. Gholizadeh, R. Saadati, W. Shatanawi S. M. Vaezpour,
Contractive mapping in generalized, ordered metric spaces with
application in integral equations, Math. Prob. Engineering. 2011
(2011) Article ID 380784.
[29] L. Gholizadeh, A xed point theorem in generalized ordered metric
spaces with its application, J. Nonlinear Sci. Appl. 6 (2013) 244{
251.