A General Fixed Point Theorem for Two Pairs of Absorbing Mappings in G_p -Metric Spaces

[1] M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), no. 1, 181–188.10.1016/S0022-247X(02)00059-8Search in Google Scholar

[2] M.R. Ahmadi Zand and A. Dehghan Nezhad, A generalization of partial metric spaces, J. Contemp. Appl. Math. 1 (2011), no. 1, 86–93.10.5402/2011/523453Search in Google Scholar

[3] J. Ali and M. Imdad, An implicit function implies several contractive conditions, Sara-jevo J. Math. 4(17) (2008), no. 2, 269–285.Search in Google Scholar

[4] I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. 157 (2010), no. 18, 2778–2785.10.1016/j.topol.2010.08.017Search in Google Scholar

[5] H. Aydi, E. Karapınar and P. Salimi, Some fixed point results in GP -metric spaces, J. Appl. Math. 2012, Art. ID 891713, 16 pp.10.5402/2012/539125Search in Google Scholar

[6] M.A. Barakat and A.M. Zidan, A common fixed point theorem for weak contractive maps in G_p-metric spaces, J. Egyptian Math. Soc. 23 (2015), no. 2, 309–314.10.1016/j.joems.2014.06.008Search in Google Scholar

[7] N. Bilgili, E. Karapınar and P. Salimi, Fixed point theorems for generalized contractions on GP -metric spaces, J. Inequal. Appl. 2013, 2013:39, 13 pp.10.1186/1029-242X-2013-39Search in Google Scholar

[8] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531–536.10.1155/S0161171202007524Search in Google Scholar

[9] K.P. Chi, E. Karapınar and T.D. Thanh, A generalized contraction principle in partial metric spaces, Math. Comput. Modelling 55 (2012), no. 5–6, 1673–1681.10.1016/j.mcm.2011.11.005Search in Google Scholar

[10] L. Ćirić, B. Samet, H. Aydi and C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), no. 6, 2398–2406.10.1016/j.amc.2011.07.005Search in Google Scholar

[11] B.C. Dhage, Generalised metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. 8 (1992), no. 4, 329–336.Search in Google Scholar

[12] B.C. Dhage, Generalized metric spaces and topological structure. I, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 46 (2000), no. 1, 3–24.Search in Google Scholar

[13] D. Gopal, A.S. Ranadive and U. Mishra, On some open problems of common fixed point theorems of noncompatible mappings, Proc. Math. Soc. BHU 20 (2004), 135–141.Search in Google Scholar

[14] D. Gopal, A.S. Ranadive and R.P. Pant, Common fixed points of absorbing maps, Bull. Marathwada Math. Soc. 9 (2008), no. 1, 43–48.Search in Google Scholar

[15] M. Imdad and S. Chauhan, Employing common limit range property to prove unified metrical common fixed point theorems, Int. J. Anal. 2013, Art. ID 763261, 10 pp.10.1155/2013/763261Search in Google Scholar

[16] M. Imdad, S. Chauhan and Z. Kadelburg, Fixed point theorem for mappings with common limit range property satisfying generalized (ψ, ϕ)-weak contractive conditions, Math. Sci. (Springer) 7 (2013), Art. 16, 8 pp.10.1186/2251-7456-7-16Search in Google Scholar

[17] M. Imdad, B.D. Pant and S. Chauhan, Fixed point theorems in Menger spaces using CLR_(S,T) property and applications, J. Nonlinear Anal. Optim. 3 (2012), no. 2, 225–237.Search in Google Scholar

[18] M. Imdad, A. Sharma and S. Chauhan, Unifying a multitude of common fixed point theorems in symmetric spaces, Filomat 28 (2014), no. 6, 1113–1132.10.2298/FIL1406113ISearch in Google Scholar

[19] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771–779.10.1155/S0161171286000935Search in Google Scholar

[20] Z. Kadelburg, H.K. Nashine and S. Radenović, Fixed point results under various contractive conditions in partial metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 107 (2013), no. 2, 241–256.10.1007/s13398-012-0066-6Search in Google Scholar

[21] E. Karapınar and U. Yüksel, Some common fixed point theorems in partial metric spaces, J. Appl. Math. 2011, Art. ID 263621, 16 pp.10.1155/2011/263621Search in Google Scholar

[22] M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), no. 1, 1–9.10.1017/S0004972700001659Search in Google Scholar

[23] Y. Liu, J. Wu and Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci. 2005, no. 19, 3045–3055.10.1155/IJMMS.2005.3045Search in Google Scholar

[24] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 62 (1977), no. 2, 344–348.10.1090/S0002-9939-1977-0436113-5Search in Google Scholar

[25] S.G Matthews, Partial metric topology, in: S. Andima et al. (eds.), Papers on General Topology and Applications, Eighth Summer Conference at Queens College, Annals of the New York Academy of Sciences, 728, New York, 1994, pp. 183–197.10.1111/j.1749-6632.1994.tb44144.xSearch in Google Scholar

[26] U. Mishra and A.S. Ranadive, Common fixed point of absorbing mappings satisfying implicit relations. Preprint.Search in Google Scholar

[27] Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl. 2008, Art. ID 189870, 12 pp.10.1155/2008/189870Search in Google Scholar

[28] Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, in: J.G. Falset et al. (eds.), International Conference on Fixed Point Theory and Applications, Proceedings of the conference held in Valencia, July 13-19, 2003, Yokohama Publishers, Yokohama, 2004, pp. 189–198.Search in Google Scholar

[29] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), no. 2, 289–297.Search in Google Scholar

[30] R.P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl. 226 (1998), no. 1, 251–258.10.1006/jmaa.1998.6029Search in Google Scholar

[31] R.P. Pant, R-weak commutativity and common fixed points of noncompatible maps, Ganita 49 (1998), no. 1, 19–27.Search in Google Scholar

[32] R.P. Pant, R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), no. 1, 37–42.Search in Google Scholar

[33] V. Parvanieh, J.R. Roshan and Z. Kadelburg, On generalized weakly GP -contractive mappings in ordered GP -metric spaces, Gulf J. Math. 1 (2013), no. 1, 78–97.10.56947/gjom.v1i1.241Search in Google Scholar

[34] V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău No. 7 (1997), 127–133.Search in Google Scholar

[35] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1999), no. 1, 157–163.10.1515/dema-1999-0117Search in Google Scholar

[36] V. Popa, A general fixed point theorem for occasionally weakly compatible mappings and applications, Sci. Stud. Res. Ser. Math. Inform. 22 (2012), no. 1, 77–91.Search in Google Scholar

[37] V. Popa, Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property, Filomat 31 (2017), no. 11, 3181–3192.10.2298/FIL1711181PSearch in Google Scholar

[38] V. Popa and M. Mocanu, Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat. 38 (2009), no. 3, 329–337.Search in Google Scholar

[39] 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 (2012), no. 2, 151–160.10.22436/jnsa.005.02.08Search in Google Scholar

[40] V. Popa and A.-M. Patriciu, Fixed point theorems for mappings satisfying an implicit relation in complete G-metric spaces, Bul. Inst. Politeh. Iaşi. Secţ. Mat. Mec. Teor. Fiz. 59(63) (2013), no. 2, 97–123.10.1007/s10013-013-0020-8Search in Google Scholar

[41] V. Popa and A.-M. Patriciu, A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Univ. Ser. Math. Inform. 29 (2014), no. 4, 351–370.Search in Google Scholar

[42] V. Popa and A.-M. Patriciu, Two general fixed point theorems for a sequence of mappings satisfying implicit relations in G_p-metric spaces, Appl. Gen. Topol. 16 (2015), no. 2, 225–231.10.4995/agt.2015.3830Search in Google Scholar

[43] V. Popa and A.-M. Patriciu, Well posedness of fixed point problem for mappings satisfying an implicit relation in G_p-metric spaces, Math. Sci. Appl. E-Notes 3 (2015), no. 1, 108–117.10.36753/mathenot.421226Search in Google Scholar

[44] V. Popa and A.-M. Patriciu, Fixed point theorems for two pairs of mappings satisfying common limit range property in G-metric spaces, Bul. Inst. Politeh. Iaşi. Secţ Mat. Mec. Teor. Fiz. 62(66) (2016), no. 2, 19–42.Search in Google Scholar

[45] V. Popa and A.-M. Patriciu, Fixed point results for pairs of absorbing mappings in partial metric spaces, Acta Univ. Apulensis Math. Inform. No. 50 (2017), 97–109.10.22190/FUMI1605969PSearch in Google Scholar

[46] V. Popa and A.-M. Patriciu, Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property in G_p-metric spaces, Ann. Math. Sil. 32 (2018), 295–312.10.2478/amsil-2018-0002Search in Google Scholar

[47] W. Shatanawi, Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces, Fixed Point Theory Appl. 2010, Art. ID 181650, 9 pp.10.1155/2010/181650Search in Google Scholar

[48] W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. 2011, Art. ID 637958, 14 pp.10.1155/2011/637958Search in Google Scholar

[49] C. Vetro and F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces, J. Nonlinear Sci. Appl. 6 (2013), no. 3, 152–161.10.22436/jnsa.006.03.01Search in Google Scholar