Common fixed points of almost generalized \((\psi,\phi)_s\)-contractive mappings in ordered \(b\)-metric spaces.

*(English)*Zbl 1295.54080Summary: In this paper, we introduce the notion of almost generalized (\(\psi\),\(\phi\))-contractive mappings and we establish some fixed and common fixed point results for this class of mappings in ordered complete \(b\)-metric spaces. Our results generalize several well-known comparable results in the literature. Finally, two examples support our results.

##### MSC:

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

47H10 | Fixed-point theorems |

54E50 | Complete metric spaces |

PDF
BibTeX
XML
Cite

\textit{J. R. Roshan} et al., Fixed Point Theory Appl. 2013, Paper No. 159, 23 p. (2013; Zbl 1295.54080)

Full Text:
DOI

##### References:

[1] | Banach, S, Sur LES operations dans LES ensembles et leur application aux equation sitegrales, Fundam. Math, 3, 133-181, (1922) · JFM 48.0201.01 |

[2] | Aghajani, A, Abbas, M, Roshan, JR: Common fixed point of generalized weak contractive mappings in partially ordered \(b\)-metric spaces. Math. Slovaca (2012, in press)Aghajani, A, Abbas, M, Roshan, JR: Common fixed point of generalized weak contractive mappings in partially ordered \(b\)-metric spaces. Math. Slovaca (2012, in press) · Zbl 1349.54078 |

[3] | Aghajani, A; Radenović, S; Roshan, JR, Common fixed point results for four mappings satisfying almost generalized [inlineequation not available: see fulltext.]-contractive condition in partially ordered metric spaces, Appl. Math. Comput, 218, 5665-5670, (2012) · Zbl 1245.54035 |

[4] | Ćirić, L, A generalization of banach’s contraction principle, Proc. Am. Math. Soc, 45, 265-273, (1974) · Zbl 0291.54056 |

[5] | Ćirić, L, On contractive type mappings, Math. Balk, 1, 52-57, (1971) · Zbl 0223.54018 |

[6] | Di Bari, C; Vetro, P, \(ϕ\)-Paris and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 57, 279-285, (2008) · Zbl 1164.54031 |

[7] | Dutta, PN; Choudhury, BS, A generalization of contraction principle in metric spaces, No. 2008, (2008) |

[8] | Kadelburg, Z; Pavlović, Z; Radenović, S, Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl, 59, 3148-3159, (2010) · Zbl 1193.54035 |

[9] | Nashine, NH; Kadelburg, Z; Radenović, S, Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, (2011) |

[10] | Nieto, JJ; Rodríguez-López, R, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013 |

[11] | Radenović, S; Kadelburg, Z, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl, 60, 1776-1783, (2010) · Zbl 1202.54039 |

[12] | Radenović, S; Kadelburg, Z; Jandrlić, D; Jandrlić, A, Some results on weakly contractive maps, Bull. Iran. Math. Soc, 38, 625-645, (2012) · Zbl 1391.54036 |

[13] | Rhoades, BE, Some theorems on weakly contractive maps, Nonlinear Anal, 47, 2683-2693, (2001) · Zbl 1042.47521 |

[14] | Samet, B; Rajović, M; Lazović, R; Stojiljković, R, Common fixed point results for nonlinear contractions in ordered partial metric spaces, No. 2011, (2011) · Zbl 1271.54086 |

[15] | Shatanawi, W, Fixed point theorems for nonlinear weakly \(C\)-contractive mappings in metric spaces, Math. Comput. Model, 54, 2816-2826, (2011) · Zbl 1235.54054 |

[16] | Shatanawi, W; Mustafa, Z; Tahat, N, Some coincidence point theorems for nonlinear contractions in ordered metric spaces, No. 2011, (2011) |

[17] | Berinde, V, Some remarks on a fixed point theorem for ćirić-type almost contractions, Carpath. J. Math, 25, 157-162, (2009) · Zbl 1249.54078 |

[18] | Berinde, V, General contractive fixed point theorems for ćirić-type almost contraction in metric spaces, Carpath. J. Math, 24, 10-19, (2008) · Zbl 1199.54209 |

[19] | Babu, GVR; Sandhya, ML; Kameswari, MVR, A note on a fixed point theorem of berinde on weak contractions, Carpath. J. Math, 24, 8-12, (2008) · Zbl 1199.54205 |

[20] | Ćirić, L; Abbas, M; Saadati, R; Hussain, N, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput, 217, 5784-5789, (2011) · Zbl 1206.54040 |

[21] | Khan, MS; Swaleh, M; Sessa, S, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc, 30, 1-9, (1984) · Zbl 0553.54023 |

[22] | Aydi, H, Common fixed point results for mappings satisfying [inlineequation not available: see fulltext.]-weak contractions in ordered partial metric spaces, Int. J. Math. Stat, 12, 53-64, (2012) |

[23] | Dorić, D, Common fixed point for generalized [inlineequation not available: see fulltext.]-weak contraction, Appl. Math. Lett, 22, 1896-1900, (2009) · Zbl 1203.54040 |

[24] | Karapinar, E; Sadarangani, K, Fixed point theory for cyclic [inlineequation not available: see fulltext.]-contractions, No. 2011, (2011) |

[25] | Nashine, NH; Samet, B, Fixed point results for mappings satisfying [inlineequation not available: see fulltext.]-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal, 74, 2201-2209, (2011) · Zbl 1208.41014 |

[26] | Nashine, NH; Samet, B; Kim, J, Fixed point results for contractions involving generalized altering distances in ordered metric spaces, No. 2011, (2011) · Zbl 1281.54034 |

[27] | Popescu, O, Fixed points for [inlineequation not available: see fulltext.]-weak contractions, Appl. Math. Lett, 24, 1-4, (2011) · Zbl 1202.54038 |

[28] | Shatanawi, W; Al-Rawashdeh, A, Common fixed points of almost generalized [inlineequation not available: see fulltext.]-contractive mappings in ordered metric spaces, No. 2012, (2012) |

[29] | Shatanawi, W; Samet, B, On [inlineequation not available: see fulltext.]-weakly contractive condition in partially ordered metric spaces, Comput. Math. Appl, 62, 3204-3214, (2011) · Zbl 1232.54041 |

[30] | Shobkolaei, N; Sedghi, S; Roshan, JR; Altun, I, Common fixed point of mappings satisfying almost generalized [inlineequation not available: see fulltext.]-contractive condition in partially ordered partial metric spaces, Appl. Math. Comput, 219, 443-452, (2012) · Zbl 1286.54055 |

[31] | Czerwik, S, Nonlinear set-valued contraction mappings in \(b\)-metric spaces, Atti Semin. Mat. Fis. Univ. Modena, 46, 263-276, (1998) · Zbl 0920.47050 |

[32] | Aydi, H; Bota, M-F; Karapınar, E; Moradi, S, A common fixed point for weak \(ϕ\)-contractions on \(b\)-metric spaces, Fixed Point Theory, 13, 337-346, (2012) · Zbl 1297.54080 |

[33] | Aydi, H; Bota, M-F; Karapınar, E; Mitrović, S, A fixed point theorem for set-valued quasi-contractions in \(b\)-metric spaces, (2012) · Zbl 06215370 |

[34] | Boriceanu, M, Fixed point theory for multivalued generalized contractions on a set with two \(b\)-metrics, Stud. Univ. Babeş-Bolyai, Math, LIV, 1-14, (2009) · Zbl 1240.54118 |

[35] | Boriceanu, M, Strict fixed point theorems for multivalued operators in \(b\)-metric spaces, Int. J. Mod. Math, 4, 285-301, (2009) · Zbl 1221.54051 |

[36] | Hussain, N; Dorić, D; Kadelburg, Z; Radenović, S, Suzuki-type fixed point results in metric type spaces, (2012) · Zbl 1274.54128 |

[37] | Hussain, N; Shah, MH, KKM mappings in cone \(b\)-metric spaces, Comput. Math. Appl, 62, 1677-1684, (2011) · Zbl 1231.54022 |

[38] | Khamsi, MA; Hussain, N, KKM mappings in metric type spaces, Nonlinear Anal, 73, 3123-3129, (2010) · Zbl 1321.54085 |

[39] | Khamsi, MA, Remarks on cone metric spaces and fixed point theorems of contractive mappings, No. 2010, (2010) · Zbl 1194.54065 |

[40] | Pacurar, M, Sequences of almost contractions and fixed points in \(b\)-metric spaces, An. Univ. Vest. Timiş., Ser. Mat.-Inform, XLVIII, 125-137, (2010) · Zbl 1249.54086 |

[41] | Roshan, JR, Shobkolaei, N, Sedghi, S, Abbas, M: Common fixed point of four maps in \(b\)-metric spaces. Hacet. J. Math. Stat. (in press)Roshan, JR, Shobkolaei, N, Sedghi, S, Abbas, M: Common fixed point of four maps in \(b\)-metric spaces. Hacet. J. Math. Stat. (in press) · Zbl 1321.54099 |

[42] | Singh, SL; Prasad, B, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl, 55, 2512-2520, (2008) · Zbl 1142.65360 |

[43] | Abbas, M; Nazir, T; Radenović, S, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett, 24, 1520-1526, (2011) · Zbl 1220.54018 |

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.