Abstract :
In this paper, tripled coincidence points of mappings satisfying $\psi$-contractiveconditions in the framework of partially ordered $G_b$-metric spaces are obtained. Our resultsextend the results of Aydi et al. [H. Aydi, E. Karapinar and W. Shatanawi, Tripled fixedpoint results in generalized metric space, J. Applied Math., Volume 2012, Article ID 314279,10 pages]. Moreover, some examples of the main result are given.
References:
[1] M. Abbas, M. Ali Khan and S. Radenovic, Common coupled xed point theorems in cone metric spaces for w-compatible mappings, Applied Math. Comput., 217, (2010), 195-202.
[2] R.P. Agarwal, E. Karapinar, Remarks on some coupled xed point theorems in G-metric spaces. Fixed Point Theory Appl, 2013, 2013:2.
[3] A. Aghajani, M. Abbas and J.R. Roshan, Common xed point of generalized weak contractive mappings in partially ordered Gb-metric spaces, Accepted in Filomat, 2013.
[4] H. Aydi, E. Karapnar and W. Shatanawi, Tripled coincidence point results for generalized contractions in ordered generalized metric spaces, Fixed Point Theory Appl., 2012, 2012:101.
[5] H. Aydi, E. Karapnar and W. Shatanawi, Tripled xed point results in generalized metric space, J. Applied Math., Volume 2012, Article ID 314279, 10 pages, doi:10.1155/2012/314279.
[6] V. Berinde, Coupled fixed point theorems for contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 75, (2012), 3218-3228.
[7] V. Berinde and M. Borcut. Tripled xed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74 (2011), 4889-4897.
[8] M. Borcut, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces. Appl. Math. Comput. 218 (2012), 7339-7346.
[9] M. Borcut and V. Berinde. Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces. Appl. Math. Comput. 218 (2012), 5929-5936.
[10] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J Modern Math. 4 (2) (2009), 285-301.
[11] Y.J. Cho, B.E. Rhoades, R. Saadati, B. Samet and W. Shatanawi, Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type, Fixed Point Theory Appl., 2012, 2012:8.
[12] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46 (1998) 263-276.
[13] H. Huang, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl, 2013:112.
[14] L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 1468-1476, 2007.
[15] N. Hussain, D. Doric, Z. Kadelburg and S. Radenovic, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., (2012), doi:10.1186/1687-1812-2012-126.
[16] M. Jleli, B. Samet, Remarks on G-metric spaces and xed point theorems, Fixed Point Theory Appl. 2012, 2012:210.
[17] B.S. Choudhury, E. Karapinar and A. Kundu. Tripled coincidence point theorems for nonlinear contractions in partially ordered metric spaces. Int. Journal of Math. and Math. Sciences, to appear.
[18] M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, Article ID 315398, 7 pages.
[19] J. Matkowski, Fixed point theorems for mapping with a contractive iterate at a point, Proceedings of the American Mathematical Society, Vol. 62, No. 2, (1997) pp. 344-348.
[20] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7(2), (2006), 289-297.
[21] V. Parvaneh, J.R. Roshan and S. Radenovic, Existence of tripled coincidence point in ordered b-metric spaces and application to a system of integral equations, Fixed Point Theory Appl.
[22] H. Rahimi, G. Soleimani Rad, P. Kumam, Coupled common fixed point theorems under weak contractions in cone metric type spaces, Thai. J. of Math. 12 (1) (2014) 1-14.
[23] S.Radenovic, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces. Banach J. Math. Anal. 5 (1) (2011) 38-50.
[24] S. Radenovic, Remarks on some recent coupled coincidence point results in symmetric G-metric spaces, Journal of Operators, Volume 2013, Article ID 290525, 8 pages.
[25] S. Radenovic, Remarks on some coupled coincidence point results in partially ordered metric spaces, Arab. J. Math. Sci., in press.
[26] S. Radenovic, S. Pantelic, P. Salimi and J. Vujakovic, A note on some tripled coincidence point results in G-metric spaces, International J. of Math. Sci. Engg. Appls., Vol. 6, No. VI, (2012), pp. 23-38.
[27] H. Rahimi, G.Soleimani Rad, Fixed point theory in various spaces, Lambert Academic Publishing, Germany, 2013.
[28] A. Rodlan, J. Martinez-Moreno, C. Rodlan, E. Karapinar, Some remarks on multidimensional fixed point theorems, Fixed Point Theory. 15 (2) (2014) 545-558.
[29] B. Rzepecki, On fixed point theorems of Maia type, Publications de lInstitut Mathematique, vol. 28 (42), 1980, pp. 179-186.
[30] B. Samet, E. Karapinar, H. Aydi, V.C. Rajic, Discussion on some coupled fixed point theorems, Fixed Point Theory Appl. 2013, 2013:50.
[31] G. Soleimani Rad, H. Aydi, P. Kumam, H. Rahimi, Common tripled fixed point results in cone metric type spaces, Rend. Circ. Mat. Palermo, 2014, DOI 10.1007/s12215-014-0158-6.
[32] G. Soleimani Rad, S. Shukla, H. Rahimi, Some relations between n-tuple fixed point and fixed point results, Revista de la Real Academia de Ciencias Exactas,Fisicas y Naturales. Serie A. Matematicas. (RACSAM), 2014, In press, DOI. 10.1007/s13398-014-0196-0.
[33] H. Rahimi, P. Vetro, G. Soleimani Rad, Some common fixed point results for weakly compatible mappings in cone metric type space, Miskolc Math. Notes. 14 (1) (2013) 233-243.