Coupled fixed point theorems for (α, φ)_g-contractive type mappings in partially ordered G-metric spaces

• Autorzy: Jianhua Chen , Xianjiu Huang
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce a new concept of (α, φ)g-contractive type mappings and establish coupled coincidence and coupled common fixed point theorems for such mappings in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of some existing results.We also give some examples to illustrate the usability of the obtained results.

Słowa kluczowe

EN

Partially ordered set; Coincidence point; Coupled fixed point; (α, φ)g-contractive type mappings; G-metric space

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-05-12

zaakceptowano

2015-09-28

online

2015-12-04

Twórcy

autor

Jianhua Chen

• Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, P. R. China and School of Mathematics
  and Statistics, Central South University, Changsha, 410083, Hunan, P. R. China

autor

Xianjiu Huang

• Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, P. R. China and School of Mathematics
  and Statistics, Central South University, Changsha, 410083, Hunan, P. R. China

Bibliografia

• [1] Mustafa Z., Sims B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 2006, 7(2), 289-297
• [2] Agarwal R.P., El-Gebeily M.A., O’Regan D., Generalized contractions in partially ordered metric spaces, Appl. Anal., 2008, 87,109-116
• [3] Bhaskar T.G., Lakshmikantham V., Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal.,2006, 65, 1379-1393
• [4] Choudhury B.S., Kundu A., A coupled coincidence point result in partially ordered metric spaces for compatible mappings,Nonlinear Anal., 2010, 73, 2524-2531[WoS]
• [5] Choudhury B.S., Maity P., Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling, 2011, 54(1-2),73-79[WoS]
• [6] C´ iric´ L.j., Cakic´ N., Rajovic´ M., Ume J.S., Monotone generalized nonlinear contractions in partially ordered metric spaces, FixedPoint Theory Appl., 2008 (2008) 11 pages. Article ID 131294.
• [7] C´ iric´ L.j., Mihet D., Saadati R., Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology Appl.,2009, 156(17), 2838-2844[WoS]
• [8] Lakshmikantham V., C´ iric´ L.j., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,Nonlinear Anal., 2009, 70, 4341-4349
• [9] Nashine H.K., Samet B., Fixed point results for mappings satisfying . (Ψ,φ)-weakly contractive condition in partially ordered metricspaces, Nonlinear Anal., 2011, 74, 2201-2209[WoS]
• [10] Samet B., Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, NonlinearAnal., 2010, 72, 4508-4517[WoS]
• [11] Jain M., Tas K., Rhoades B.E., Gupta N., Coupled fixed point theorems for generalized symmetric contractions in partially orderedmetric spaces and applications, J. Comput. Appl. Anal., 2014, 16(3), 438-454
• [12] Shatanawi W., Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl., 2010, 60, 2508-2515[WoS]
• [13] Abbas M., Khan M.A., Radenovi´c S., Common coupled fixed point theorem in cone metric space for w*-compatible mappings,Appl. Math. Comput., 2010, 217, 195-202[WoS]
• [14] Mohiuddine S.A., Alotaibi A., Coupled coincidence point theorems for compatible mappings in partially ordered intuitionisticgeneralized fuzzy metric spaces, Fixed Point Theory Appl., 2013, 265 (2013)[Crossref][WoS]
• [15] Aydi H., Damjanovi´c B., Samet B., Shatanawi W., Coupled fixed point theorems for nonlinear contractions in partially orderedG-metric spaces, Math. Comput. Modelling, 2011, 54, 2443-2450[WoS]
• [16] Luong N.V„ Thuan N.X., Coupled fixed point theorems in partially ordered G-metric spaces, Math. Comput. Modelling, 2012, 55,1601-1609[WoS]
• [17] Chugh R., Kadian T., Rani A., Rhoades B.E., Property P in G-metric spaces, Fixed Point Theory Appl., 2010 (2010) 12. ArticleID 401684[Crossref]
• [18] Shatanawi W., Fixed point theory for contractive mappings satisfying φ-maps in G-metric spaces, Fixed Point Theory Appl., 2010 (2010) 9. Article ID 181650[WoS][Crossref]
• [19] Mustafa Z., Obiedat H., Awawdeh F., Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point TheoryAppl., 2008 (2008) 12. Article ID 189870[Crossref][WoS]
• [20] Mustafa Z., Shatanawi W., Bataineh M., Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., 2009 (2009)10. Article ID 283028
• [21] Mustafa Z., Sims B., Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., 2009(2009) 10. Article ID 917175[Crossref]
• [22] Nashine H.K., Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 2012, 1, 1-13
• [23] Karapinar E., Kumam P., Merhan I., Coupled fixed point theorems on partially ordered G-metric spaces, Fixed Point Theory Appl.,2012, 174 (2012)[Crossref]
• [24] Samet B., Vetro C., Vetro P., Fixed point theorems for α-Ψ-contractive type mappings, Nonlinear Anal., 2012, 75, 2154-2165
• [25] Mursaleen M., Mohiuddine S.A., Agarwal R.P., Coupled fixed point theorems for α-Ψ-contractive type mappings in partiallyordered metric spaces, Fixed Point Theory Appl., 2012, 228 (2012)[Crossref]
• [26] Ali M.U., Kamram T., karapinar E., Fixed point of α-Ψ-mappings in uniform spaces, Fixed Point Theory Appl., 2014, 150 (2014)[Crossref]
• [27] Chen J.H., Huang X.J., Coupled fixed point theorems for compatible mappings in partially ordered G-metric spaces, J. NonlinearSci. Appl., 2015, 8(2), 130-141
• [28] Chen J.H., Huang X.J., Quadruple fixed point theorems under (Ψ,φ)-contractive conditions in partially ordered G-metric spaceswith mixed g-monotone property, J. Nonlinear Sci. Appl., 2015, 8(4), 285-300

Identyfikatory

DOI

10.1515/math-2015-0082