Some new coupled fixed point theorems in ordered partial \(b\)-metric spaces

Volume 9, Issue 12, pp 5931--5949 http://dx.doi.org/10.22436/jnsa.009.12.03

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2483 Downloads
• 3359 Views

Authors

Hedong Li - Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China. Feng Gu - Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.

Abstract

In this paper, we establish some new coupled fixed point theorems in ordered partial \(b\)-metric spaces. Also, an example is provided to support our new results. The results presented in this paper extend and improve several well-known comparable results.

Share and Cite

Keywords

• Common coupled fixed point
• coupled coincidence point
• partially ordered set
• mixed \(g\)-monotone property
• partial \(b\)-metric space.

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, M. Ali Khan, S. Radenović, Common coupled fixed point theorems in cone metric spaces for w- compatible mappings, Appl. Math. Comput., 217 (2010), 195--202


• [2] T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923--2927


• [3] T. Abdeljawad, E. Karapınar, K. Taş, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900--1904


• [4] A. Aghajani, R. Arab, Fixed points of (\(\psi,\phi,\theta\))-contractive mappings in partially ordered b-metric spaces and application to quadratic integral equations, Fixed Point Theory Appl., 2013 (2013), 20 pages


• [5] M. Akkouchi, A common fixed point theorem for expansive mappings under strict implicit conditions on b-metric spaces, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 50 (2011), 5--15


• [6] H. Aydi, E. Karapınar, W. Shatanawi, Coupled fixed point results for \(\phi,\psi\) -weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl., 62 (2011), 4449--4460


• [7] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5--11


• [8] R. George, K. P. Reshma, A. Padmavati, Fixed point theorems for cyclic contractions in b-metric spaces, J. Nonlinear Funct. Anal., 2015 (2015), 22 pages


• [9] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379--1393


• [10] A. Gupta, P. Gautam, Some coupled fixed point theorems on quasi-partial b-metric spaces, Int. J. Math. Anal., 9 (2015), 293--306


• [11] J. Harjani, B. López, K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal., 74 (2011), 1749--1760


• [12] M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1--9


• [13] J. K. Kim, T. M. Tuyen, Approximation common zero of two accretive operators in Banach spaces, Appl. Math. Comput., 283 (2016), 265--281


• [14] V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341--4349


• [15] H. Li, F. Gu, A new common fixed point theorem for four maps in b-metric spaces, J. Hangzhou Norm. Univ., Nat. Sci. Ed., 15 (2016), 75--80


• [16] L. Liu, F. Gu, The common fixed point theorem for a class of twice power type \(\Phi\)-contractive mapping in b-metric spaces, J. Hangzhou Norm. Univ., Nat. Sci. Ed., 15 (2016), 171--177


• [17] N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal., 74 (2011), 983--992


• [18] Partial metric topology, Papers on general topology and applications, S. G. Matthews, Flushing, NY, (1992), 183-197, Ann. New York Acad. Sci., New York Acad. Sci., New York (1994)


• [19] Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 26 pages


• [20] H. K. Nashine, W. Shatanawi, Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl., 62 (2011), 1984--1993


• [21] X. L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 9 pages


• [22] H. Piri, Some Suzuki type fixed point theorems in complete cone b-metric spaces over a solid vector space, Commun. Optim. Theory, 2016 (2016), 15 pages


• [23] K. P. R. Rao, K. V. Siva Parvathi, M. Imdad, A coupled coincidence point theorem on ordered partial b-metric-like spaces, Electron. J. Math. Anal. Appl., 3 (2015), 141--149


• [24] J. R. Roshan, V. Parvaneh, I. Altun, Some coincidence point results in ordered b-metric spaces and applications in a system of integral equations, Appl. Math. Comput., 226 (2014), 725--737


• [25] G. S. Saluja, Some fixed point theorems for generalized contractions involving rational expressions in b-metric spaces, Commun. Optim. Theory, 2016 (2016), 13 pages


• [26] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2013), 703--711


• [27] J. Zhao, S. Wang, Viscosity approximation method for the split common fixed point problem of quasi-strict pseu- docontractions without prior knowledge of operator norms, Noninear Funct. Anal. Appl., 20 (2015), 199--213