##
**Some fixed point results in \(GP\)-metric spaces.**
*(English)*
Zbl 1266.54084

Summary: Following a recent paper of Zand and Nezhad (2011), we establish some fixed point results in \(GP\)-metric spaces. The presented theorems generalize and improve several existing results in the literature. Also, some examples are presented.

### MSC:

54H25 | Fixed-point and coincidence theorems (topological aspects) |

PDF
BibTeX
XML
Cite

\textit{H. Aydi} et al., J. Appl. Math. 2012, Article ID 891713, 15 p. (2012; Zbl 1266.54084)

Full Text:
DOI

### References:

[1] | S. G. Matthews, “Partial metric topology,” Annals of the New York Academy of Sciences, vol. 728, Proceedings of the 8th Summer Conference on General Topology and Applications, pp. 183-197, 1994. · Zbl 0911.54025 |

[2] | S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133-181, 1922. · JFM 48.0201.01 |

[3] | T. Abedelljawad, E. Karapınar, and K. Ta\cs, “Existence and uniqueness of common fixed point on partial metric spaces,” Applied Mathematics Letters, vol. 24, pp. 1894-1899, 2011. · Zbl 1229.54056 |

[4] | T. Abdeljawad, E. Karapınar, and K. Ta\cs, “A generalized contraction principle with control functions on partial metric spaces,” Computers & Mathematics with Applications, vol. 63, no. 3, pp. 716-719, 2012. · Zbl 1238.54017 |

[5] | I. Altun, F. Sola, and H. Simsek, “Generalized contractions on partial metric spaces,” Topology and its Applications, vol. 157, no. 18, pp. 2778-2785, 2010. · Zbl 1207.54052 |

[6] | H. Aydi, “Some coupled fixed point results on partial metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2011, Article ID 647091, 11 pages, 2011. · Zbl 1213.54060 |

[7] | H. Aydi, “Some fixed point results in ordered partial metric spaces,” Journal of Nonlinear Science and its Applications, vol. 4, no. 3, pp. 210-217, 2011. · Zbl 1489.54068 |

[8] | H. Aydi, “Fixed point results for weakly contractive mappings in ordered partial metric spaces,” Journal of Advanced Mathematical Studies, vol. 4, no. 2, pp. 1-12, 2011. · Zbl 1234.54051 |

[9] | H. Aydi, “Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces,” Journal of Nonlinear Analysis and Optimization, vol. 2, no. 2, pp. 33-48, 2011. · Zbl 1413.54102 |

[10] | H. Aydi, E. Karapınar, and W. Shatanawi, “Tripled fixed point results in generalized metric spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 314279, 10 pages, 2012. · Zbl 1244.54085 |

[11] | H. Aydi, “Common fixed point results for mappings satisfying (\psi , \varphi )-weak contractions in ordered partial metric spaces,” International Journal of Mathematics and Statistics, vol. 12, no. 2, pp. 53-64, 2012. · Zbl 1306.54041 |

[12] | L. Ćirić, B. Samet, H. Aydi, and C. Vetro, “Common fixed points of generalized contractions on partial metric spaces and an application,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2398-2406, 2011. · Zbl 1244.54090 |

[13] | K. P. Chi, E. Karapınar, and T. D. Thanh, “A generalized contraction principle in partial metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 56, pp. 1673-1681, 2012. · Zbl 1255.54020 |

[14] | C. Di Bari, M. Milojević, S. Radenović, and P. Vetro, “Common fixed points for self-mappings on partial metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 140, 2012. · Zbl 1277.54031 |

[15] | E. Karapınar and M. Erhan, “Fixed point theorems for operators on partial metric spaces,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1894-1899, 2011. · Zbl 1229.54056 |

[16] | E. Karapınar, “Generalizations of Caristi Kirk’s theorem on partial metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 4, 2011. · Zbl 1281.54027 |

[17] | E. Karapınar, “Weak \varphi -contraction on partial metric spaces,” Journal of Computational Analysis and Applications, vol. 14, no. 2, pp. 206-210, 2012. · Zbl 1246.54045 |

[18] | E. Karapınar and U. Yüksel, “Some common fixed point theorems in partial metric spaces,” Journal of Applied Mathematics, vol. 2011, Article ID 263621, 16 pages, 2011. · Zbl 1238.54027 |

[19] | E. Karapınar, “A note on common fixed point theorems in partial metric spaces,” Miskolc Mathematical Notes, vol. 12, no. 2, pp. 185-191, 2011. |

[20] | H. K. Nashine, Z. Kadelburg, and S. Radenović, “Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces,” Mathematical and Computer Modelling. In press. · Zbl 1286.54051 |

[21] | S. Oltra and O. Valero, “Banach’s fixed point theorem for partial metric spaces,” Rendiconti dell’Istituto di Matematica dell’Università di Trieste, vol. 36, no. 1-2, pp. 17-26, 2004. · Zbl 1080.54030 |

[22] | S. Romaguera, “A Kirk type characterization of completeness for partial metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 493298, 6 pages, 2010. · Zbl 1193.54047 |

[23] | O. Valero, “On Banach fixed point theorems for partial metric spaces,” Applied General Topology, vol. 6, no. 2, pp. 229-240, 2005. · Zbl 1087.54020 |

[24] | Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289-297, 2006. · Zbl 1111.54025 |

[25] | M. Abbas, A. R. Khan, and T. Nazir, “Coupled common fixed point results in two generalized metric spaces,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6328-6336, 2011. · Zbl 1210.54048 |

[26] | M. Abbas, T. Nazir, and D. Dorić, “Common fixed point of mappings satisfying (E.A) property in generalized metric spaces,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7665-7670, 2012. · Zbl 1244.54083 |

[27] | H. Aydi, E. Karapınar, and W. Shatanawi, “Tripled common fixed point results for generalized contractions in ordered generalized metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 101, 2012. · Zbl 1420.54070 |

[28] | H.-S. Ding and E. Karapınar, “A note on some coupled fixed point theorems on G-metric space,” Journal of Inequalities and Applications, vol. 2012, article 170, 2012. · Zbl 1275.54029 |

[29] | Z. Mustafa and B. Sims, “Some remarks concerninig D-metric spaces,” in Proceedings of the Internatinal Conferences on Fixed Point Theorey and Applications, pp. 189-198, Valencia, Spain, July 2003. · Zbl 1079.54017 |

[30] | Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory [Ph.D. thesis], The University of Newcastle, Callaghan, Australia, 2005. |

[31] | Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 189870, 12 pages, 2008. · Zbl 1148.54336 |

[32] | Z. Mustafa, W. Shatanawi, and M. Bataineh, “Existence of fixed point results in G-metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 283028, 10 pages, 2009. · Zbl 1179.54066 |

[33] | Z. Mustafa and H. Obiedat, “A fixed point theorem of Reich in G-metric spaces,” Cubo, vol. 12, no. 1, pp. 83-93, 2010. · Zbl 1220.54030 |

[34] | Z. Mustafa and B. Sims, “Fixed point theorems for contractive mappings in complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 917175, 10 pages, 2009. · Zbl 1179.54067 |

[35] | Z. Mustafa, M. Khandagji, and W. Shatanawi, “Fixed point results on complete G-metric spaces,” Studia Scientiarum Mathematicarum Hungarica, vol. 48, no. 3, pp. 304-319, 2011. · Zbl 1249.54084 |

[36] | Z. Mustafa, F. Awawdeh, and W. Shatanawi, “Fixed point theorem for expansive mappings in G-metric spaces,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 49-52, pp. 2463-2472, 2010. · Zbl 1284.54065 |

[37] | Z. Mustafa, H. Aydi, and E. Karapınar, “On common fixed points in G-metric spaces using (E.A) property,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 1944-1956, 2012. · Zbl 1268.54027 |

[38] | Z. Mustafa, H. Aydi, and E. Karapınar, “Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 71, 2012. · Zbl 1273.54067 |

[39] | R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, “Fixed point theorems in generalized partially ordered G-metric spaces,” Mathematical and Computer Modelling, vol. 52, no. 5-6, pp. 797-801, 2010. · Zbl 1202.54042 |

[40] | W. Shatanawi, “Fixed point theory for contractive mappings satisfying \Phi -maps in G-metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 181650, 9 pages, 2010. · Zbl 1204.54039 |

[41] | N. Tahat, H. Aydi, E. Karapınar, and W. Shatanawi, “Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 48, 2012. · Zbl 1273.54078 |

[42] | W. Shatanawi, “Some fixed point theorems in ordered G-metric spaces and applications,” Abstract and Applied Analysis, vol. 2011, Article ID 126205, 11 pages, 2011. · Zbl 1217.54057 |

[43] | M. R. A. Zand and and A. D. Nezhad, “A generalization of partial metric spaces,” Journal of Contemporary Applied Mathematics, vol. 24, pp. 86-93, 2011. |

[44] | D. Ilić, V. Pavlović, and V. Rako, “Some new extensions of Banach’s contraction principle to partial metric space,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1326-1330, 2011. · Zbl 1292.54025 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.