Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces

Volume 7, Issue 4, pp 229--245
• 1181 Views

Authors

Jamal Rezaei Roshan - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran. Vahid Parvaneh - Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran. Zoran Kadelburg - Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia.

Abstract

The aim of this paper is to present some common fixed point theorems for g-weakly isotone increasing mappings satisfying a generalized contractive type condition under a continuous function in the framework of ordered b-metric spaces. Our results extend the results of Nashine et al. [H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling 54 (2011) 712-720] from the context of ordered metric spaces to the setting of ordered b-metric spaces. Moreover, some examples of applications of the main result are given. Finally, we establish an existence theorem for a solution of an integral equation.

Share and Cite

ISRP Style

Jamal Rezaei Roshan, Vahid Parvaneh, Zoran Kadelburg, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 4, 229--245

AMA Style

Roshan Jamal Rezaei, Parvaneh Vahid, Kadelburg Zoran, Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces. J. Nonlinear Sci. Appl. (2014); 7(4):229--245

Chicago/Turabian Style

Roshan, Jamal Rezaei, Parvaneh, Vahid, Kadelburg, Zoran. "Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces." Journal of Nonlinear Sciences and Applications, 7, no. 4 (2014): 229--245

Keywords

• Common xed point
• b-metric space
• partially ordered set
• weakly isotone increasing mappings.

•  47H10
•  54H25

References

• [1] M. Abbas, V. Parvaneh, A. Razani, Periodic points of T- Ćirić generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19 (2012), 597-610.

• [2] R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Applicable Anal., 87 (2008), 109-116.

• [3] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, to appear in Math. Slovaca., ()

• [4] A. Aghajani, S. Radenović, J. R. Roshan, Common fixed point results for four mappings satisfying almost generalized (S; T)-contractive condition in partially ordered metric spaces, Appl. Math. Comput., 218 (2012), 5665-5670.

• [5] I. Altun, B. Damjanović, D. -Dorić, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23 (2009), 310-316.

• [6] I. Altun, H. Simsek , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., Article ID 621492, 2010 (2010), 17 pages.

• [7] H. Aydi , Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4 (2011), 210-217.

• [8] B. S. Choudhury, N. Matiya, P. Maity, Coincidence point results of multivalued weak C-contractions on metric spaces with a partial order, J. Nonlinear Sci. Appl., 6 (2013), 7-17.

• [9] L. Ćirić, N. Cakić, M. Rajović, J. S. Ume , Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., Article ID 131294, 2008 (2008), 11 pages.

• [10] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993), 5-11.

• [11] J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197.

• [12] N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012:126 (2012)

• [13] N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic ( $\psi,\varphi,L, A,B$)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013:256 (2013), 18 pages.

• [14] N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684.

• [15] G. S. Jeong, B. E. Rhoades, Maps for which $F(T) = F(T^n)$, Fixed Point Theory Appl., 6 (2005), 87-131.

• [16] M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., Article ID 978121, 2010 (2010), 15 pages.

• [17] M. A. Khamsi , Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., Article ID 315398, 2010 (2010), 7 pages.

• [18] A. Mukheimer, $\alpha-\psi-\varphi$-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 168-179.

• [19] H. K. Nashine , Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., 1 (2012), 1-13.

• [20] H. K. Nashine, Z. Kadelburg, S. Radenović, Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, 57 (2013), 2355-2365.

• [21] H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling, 54 (2011), 712-720.

• [22] J. J. Nieto, R. Rodríguez-Lépez, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica (Engl. Ser.), 23 (2007), 2205-2212.

• [23] M. Pacurar , Sequences of almost contractions and fixed points in b-metric spaces, Anal. Univ. de Vest, Timisoara Seria Matematica Informatica, XLVIII , (2010), 125-137.

• [24] S. Radenović, Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl., 60 (2010), 1776-1783.

• [25] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi , Common fixed points of almost generalized $(\psi,\varphi)_s$-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013:159 (2013), 23 pages.

• [26] S. L. Singh, B. Prasad , Some coincidence theorems and stability of iterative procedures , Comput. Math. Appl., 55 (2008), 2512-2520.

• [27] M. P. Stanić, A. S. Cvetković, Su. Simić, S. Dimitrijević , Common fixed point under contractive condition of Ćirić's type on cone metric type space, Fixed Point Theory Appl., 2012:35 (2012), 7 pages.