Fixed points for a pair of weakly compatible mappings satisfying a new type of ϕ - implicit relation in S - metric spaces

[1] M. Abbas and B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215 (5) (2009), 262–269.10.1016/j.amc.2009.04.085Search in Google Scholar

[2] J. M. Afra, Fixed point theorems in S - metric spaces, Theory Approx. Appl., 10 (1) (2014), 57–68.10.1186/1687-1812-2014-43Search in Google Scholar

[3] I. Altun and D. Turkoglu, Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanesse J. Math., 13 (4) (2009), 1291–1304.10.11650/twjm/1500405509Search in Google Scholar

[4] G. V. R. Babu and B. K. Leta, Fixed points of (α, ψ, ϕ) - generalized weakly contractive maps and property (P) in S - metric spaces, Filomat, 31 (14) (2017), 4469–4481.10.2298/FIL1714469BSearch in Google Scholar

[5] B. C. Dhage, Generalized metric space and mappings with fixed point, Bull. Calcutta Math. Soc., 84 (1992), 329–336.Search in Google Scholar

[6] B. C. Dhage, Generalized metric space and topological structures I, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Mat., 46 (1) (2000), 3–20.Search in Google Scholar

[7] N. V. Dung, N. T. Hieu, S. Radojević, Fixed point theorems for g -monotone maps on partially ordered S - metric spaces, Filomat, 28 (9) (2014), 1885–1898.10.2298/FIL1409885DSearch in Google Scholar

[8] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), 771–779.10.1155/S0161171286000935Search in Google Scholar

[9] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (2) (1997), 344–348.10.1090/S0002-9939-1977-0436113-5Search in Google Scholar

[10] Z. Mustafa, Common fixed point of weakly compatible mappings in G -metric spaces, Appl. Math. Sci., 92, 6 (2006), 4589–4601.Search in Google Scholar

[11] Z. Mustafa and B. Sims, Some remarks concerning D - metric spaces, Proc. Conf. Fixed Point Theory Appl., Valencia (Spain), 2013, 189–198.Search in Google Scholar

[12] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 280–297.Search in Google Scholar

[13] N. Y. Özgür and N. Taş, Some generalizations on fixed point theorems on S - metric spaces, In: Rassias T., Pardalos P. (eds) Essays in Mathematics and its Applications. Springer, Cham, 229–261.10.1007/978-3-319-31338-2_11Search in Google Scholar

[14] V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. Ştiinţ. Ser. Mat., Univ. Bacău, 7 (1997), 129–133.Search in Google Scholar

[15] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math., 32 (1) (1999), 157–163.10.1515/dema-1999-0117Search in Google Scholar

[16] V. Popa, A general fixed point theorem for several mappings in G -metric spaces, Sci. Stud. Res. Ser. Math. Inform., 32 (1) (2011), 205–214.Search in Google Scholar

[17] V. Popa and A.-M. Patriciu, A general fixed point theorem for pairs of weakly compatible mappings in G - metric spaces, J. Nonlinear Sci. Appl., 5 (2) (2012), 151–160.10.22436/jnsa.005.02.08Search in Google Scholar

[18] V. Popa and A.-M. Patriciu, A general fixed point theorem for mappings satisfying an φ - implicit relation in G - metric spaces, Gazi Univ. J. Sci., 25 (2012), 401–408.Search in Google Scholar

[19] K. Prudhvi, Fixed point results in S - metric spaces, Univer. J. Comput. Math., 3 (2015), 19–21.10.13189/ujcmj.2015.030201Search in Google Scholar

[20] K. Prudhvi, Some fixed point results in S - metric spaces, J. Math. Sci. Appl., 4 (1) (2016), 1–3.Search in Google Scholar

[21] S. Sedghi and N. V. Dung, Fixed point theorems on S - metric spaces, Mat. Vesn., 66 (1) (2014), 113–124.10.1186/1687-1812-2014-43Search in Google Scholar

[22] S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in S - metric spaces, Mat. Vesn., 64 (3) (2012), 258–266.Search in Google Scholar

[23] S. Sedghi, M. M. Rezaee, T. Došenović, S. Radenović, Common fixed point theorems for contractive mappings satisfying φ - maps in S -metric spaces, Acta Univ. Sapientiae, Math., 8 (2) (2016), 298–311.10.1515/ausm-2016-0020Search in Google Scholar