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 AM  Vol.7 No.5 , March 2016
Study of Fixed Point Theorems for Higher Dimension in Partially Ordered Metric Spaces
Abstract: In this paper, we establish the existence and uniqueness of fixed points of operator , when n is an arbitrary positive integer and X is a partially ordered complete metric space. We have shown examples to verify our work. Our results generalize the recent fixed point theorems cited in [1]-[4] etc. and include several recent developments.
Cite this paper: Masmali, I. and Dalal, S. (2016) Study of Fixed Point Theorems for Higher Dimension in Partially Ordered Metric Spaces. Applied Mathematics, 7, 399-412. doi: 10.4236/am.2016.75037.
References

[1]   Choudhary, B.S. and Kundu, A. (2010) Coupled Coincidence Point Results in Ordered Metric Spaces for Compatible Mappings. Nonlinear Analysis: Theory, Method and Applications A, 73, 2524-2531.
http://dx.doi.org/10.1016/j.na.2010.06.025

[2]   Choudhary, B.S., Das K. and Das, P. Coupled Coincidence Point Theorems in Partially Ordered Fuzzy Metric Spaces, Fuzzy Sets and System ( in Press).

[3]   Bhaskar, T.G. and Lakshmikantham, V. (2006) Fixed Point Theorems in Partially Ordered Metric Spaces and Applications. Nonlinear Analysis: Theory, Methods and Applications, 65, 1379-1393.
http://dx.doi.org/10.1016/j.na.2005.10.017

[4]   Lakshmikantham, V. and Ciric, L. (2009) Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces. Nonlinear Analysis: Theory, Method and Applications, 70, 4341-4349.
http://dx.doi.org/10.1016/j.na.2008.09.020

[5]   Alotaibi, A. and Alsulami, S. (2011) Coupled Coincidence Points for Monotone Operators in Partially Ordered Metric Spaces. Fixed Point Theory and Applications, 2011, 44.
http://dx.doi.org/10.1186/1687-1812-2011-44

[6]   Ran, A.C.M. and Reuring, M.C.B. (2004) A Fixed Point Theorem in Partially Metric Spaces and Some Applications in Partially Ordered Metric Spaces. Proceedings of the American Mathematical Society, 132, 1435-1443.
http://dx.doi.org/10.1090/S0002-9939-03-07220-4

[7]   Karapinar, E., Luong, N.V. and Thuan, N.X. (2012) Coupled Coincidence Points for Mixed Monotone Operators in Partially Ordered Metric Spaces. Arabian Journal of Mathematics, 1, 329-339.
http://dx.doi.org/10.1007/s40065-012-0027-0

[8]   Karapinar, E. and Irhan, I.M. (1999) Fixed Point Theorems for Operators on Partial Metric Spaces. Appl. Categ, Structures, 7, 71-83.
http://dx.doi.org/10.1023/A:1008684018933

[9]   Jungck, G. (1986) Compatible Mappings and Common Fixed Points. International Journal of Mathematics and Mathematical Sciences, 9, 771-779.
http://dx.doi.org/10.1155/S0161171286000935

[10]   Aydi, H. (2011) Some Coupled Fixed Point Results on Partial Metric Spaces. International Journal of Mathematics and Mathematical Sciences, 2011, Article ID: 647091, 11 p.

[11]   Nieto, J.J. and Rodriguez-Lopez, R. (2005) Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equation. Order, 22, 223-239.
http://dx.doi.org/10.1007/s11083-005-9018-5

[12]   Sumitra, D., Manro, S., Bhatia, S.S., Kumar, S. and Kumum, P. (2013) Weakly Compatibly Mapping with CLRS Mapping in Fuzzy Metric Saces. Journal Nonlinear Analysis and Applications, 2013, 1-12.
http://dx.doi.org/10.5899/2013/jnaa-00206

[13]   Gugani, M., Agarwal, M. and Chugh, R. (2012) Common Fixed Point Results in G-Metric Spaces and Applications. International Journal of Computer Applications, 43, No. 11.

[14]   Nguyen, V. and Nguyen, X. (2010) Coupled Fixed Point Theorems in Partially Ordered Metric Spaces. Bulletin of Mathematical Analysis and Applications, 2, 16-24.

[15]   Berinde, V. and Borcut, M. (2011) Tripled Fixed Point Theorems for Contractive Type Mappings in Partially Ordered Metric Spaces. Nonlinear Analysis, 74, 4889-4897.
http://dx.doi.org/10.1016/j.na.2011.03.032

[16]   Karpinar, E. (2012) Quartet Fixed Point for Nonlinear Contraction.
http://arxiv.org/abs/1106.5472

[17]   Sumitra, D., Chaun, S. and Pant, B.D. (2013) Coincidence and Common Fixed Point Theorems in Intutionistic Fuzzy –Metric Spaces. Far East Journal of Mathematical Science, 79, 25-48.

[18]   Sumitra, D., Chauhan, S. and Kadelburg, Z. (2013) A Common Fixed Point Theorem in Metric Space under General Contractive Condition. Journal of Applied Mathematics, 2013, Article ID: 510691, 7 p.

[19]   Sumitraand Manro, S. (2014) Coincidence and Common Fixed Point of Weakly Compatible Maps in Fuzzy Metric Spaces. Applied Mathematics, 5, 1335-1348.

[20]   Sumitra, D., Imdad, M. and Chauhan, S. (2013) Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces. Abstract and Applied Analysis, 2013, Article ID: 413473, 11 p.

[21]   Shatanawi, W. (2011) Coupled Fixed Point Theorems in Generalized Metric Spaces. Hacettepe Journal of Mathematics and Statistics, 40, 441-447.

[22]   Imdad, M., Soliman, A.H., Choudhary, B.S. and Das, P. (2013) On n-Tupled Coincidence Point Results in Metric Spaces. Journal of Operators, 2013, Article ID: 532867, 8 p.

[23]   Jungck, G. (1976) Commuting Mappings and Fixed Point. American Mathematical Monthly, 83, 261-263.
http://dx.doi.org/10.2307/2318216

 
 
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