Open Access
SOME COUPLED FIXED POINT THEOREMS FOR MAPPINGS IN PARTIALLY ORDERED G-METRIC SPACES BY USING A RATIONAL TYPE CONTRACTIVE CONDITION
Nurcan Bilgili Güngör1*
1Amasya University, Amasya, Turkey
* Corresponding author: bilgilinurcan@gmail.com

Presented at the 3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences) (ISAS2019-ENS), Ankara, Turkey, Apr 19, 2019

SETSCI Conference Proceedings, 2019, 4, Page (s): 343-350 , https://doi.org/

Published Date: 01 June 2019    | 705     6

Abstract

Coupled fixed point results for nonlinear contraction mappings having a mixed monotone property in a partially ordered G-metric space due to Choudhury and Maity are extended and unified. In this paper, some corresponding coupled fixed point theorems are obtained in partially ordered Gmetric spaces by employing a rational type contractive condition. These results generalize and extend some recently announced results in the literature.

Keywords - -

References

[1] Abbas, M, Rhoades, BE: Common fixed point results for noncommuting mappings without continuity in generalised metric spaces, Appl. Math. Comput. 215 (2009), 262-269.

[2] Abbas, M, Nazir, T, Radenovic, S: Some periodic point results in generalized metric spaces, Appl. Math. Comput. 217 (8) (2010), 4094-4099.

[3] Bhaskar, TG, Lakshmikantham, V: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods and Applications 65 (7) (2006), 1379-1393.

[4] Chakrabarti, K: Fixed point theorems in G-metric spaces with W maps, Mathematical Sciences Letters, 2 (2013), 29-35.

[5] Chakrabarti, K: Coupled fixed point theorems with rational type contractive condition on a partially ordered Gmetric space, Journal of Math. Article ID 785457, 7 pages (2014).

[6] Chang, SS, Ma, YH: Coupled fixed point of mixed monotone condensing operators and existence theorem of the solution for a class of functional equations arising in dynamic programming, J. Math. Anal. Appl. 160 (1991),468-479.

[7] Chen, CM : Common fixed point theorems in complete generalized metric spaces, Journal of Applied Mathematics, vol. 2012, Article ID 945915, 14 pages, 2012.

[8] Choudhury, BS, Maity, P: Coupled fixed point results in generalized metric spaces, Math. Comput. Model. 54 (2011), 73-79.

[9] Chugh, R, Kadian, T, Rani, A, Rhoades, BE: Property P in G-metric spaces, Fixed Point Theory Appl. 2010, Article ID 401684, 12 (2010).

[10] Ciric, L, Olatinwo, MO, Gopal, D, Akinbo, G: Coupled fixed point theorems for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Advances in Fixed Point Theory, 2 (1) (2012), 1-8.

[11] Harjani, J, Lopez, B, Sadarangani, K: A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric spaces, Abstract and Applied Analysis, Volume (2010), Article ID 190701, 8 pages.

[12] Lakshmikantham, V, Ciric, L: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods and Applications, 70 (12) (2009), 4341-4349.

[13] Mustafa, Z, Sims, B: Some remarks concerning D-metric spaces, Proc Int. Conf. on Fixed Point Theor. Appl.,Valencia, Spain.(2003) 189-198.

[14] Mustafa, Z, Sims, B: A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.

[15] Mustafa, Z, Obiedat, H, Awawdeh, F: Some of fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008, Article ID 189870, 12 (2008).

[16] Mustafa, Z, Shatanawi, W, Bataineh, M: Fixed point theorems on uncomplete G-metric spaces, J. Math. Stat. 4 (2008), 196-201.

[17] Mustafa, Z, Shatanawi, W, Bataineh, M: Existence of fixed point result in G-metric spaces, Int. J. Math. Sci, 2009, Article ID 283028, 10 (2009).

[18] Mustafa, Z, Sims, B: Fixed point theorems for contractive mappings in complete G-metric space. Fixed Point Theory Appl., 2009, Article ID 917175, 10 (2009).

[19] Saadati, R, Voezpour, SM, Vetro, P, Rhoades, BE: Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Model. 52 (2010), 797-801.

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