• Ljiljana Paunović Teacher Education School in Prizren-Leposavić, University of Priština, Leposavić, Serbia.
Keywords: b-metric spaces, compatible mappings, P-increasing, integral equation, C-class functions,


Fixed point theorems for monotone operators in ordered metric spaces are widely investigated and have found various applications in differential and integral equations (Nieto & Rodríguez-Lόpez, 2005), (Nieto & Rodríguez-Lόpez, 2007), (Wu, 2008). Motivated by the work in (Agarwal et al., 2012) and (Luong & Thuan, 2011) we study the existence of solutions for a system of nonlinear integral equations in ordered b-metric spaces using the results given in this paper.


Author Biography

Ljiljana Paunović, Teacher Education School in Prizren-Leposavić, University of Priština, Leposavić, Serbia.

Docent na Učiteljskom fakultetu, naučna oblast   Matematika, magistratura iz oblasti numeričke analize (odbranjen magistarski rad na Prirodno-matematičkom fakultetu u Kragujevcu), doktorat iz oblasti funkcionalne analize (odbranjen na pmf-u u Kragujevcu).



Agarwal, R.P., Hussain, N., & Taoudi, M.A. 2012. Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations. Abstr. Appl. Anal., . Article ID 245872, 15 pages.

Akkouchi, M. 2011. Common fixed point theorems for two selfmappings of a b-metric space under an implicit relation. Hacet. J. Math. Statist., 40(6), pp. 805-810.

Aydi, H., Bota, M., Karapinar, E., & Mitrović, S. 2012. A fixed point theorem for set-valued quasi-contractions in b-metric spaces. Fixed Point Theory Appl., 88.

Ansari, A.H., Chandok, S., & Ionescu, C. 2014. Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions. J. Inequal. Appl., 429.

Aghajani, A., Abbas, M., & Roshan, J.R. 2014. Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces. Math. Slov., 4, pp. 941-960.

Bhaskar, T.G., & Lakshmikantham, V. 2006. Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal., 65, pp. 1379-1393.

Boriceanu, M. 2009. Strict fixed point theorems for multivalued operators in b-metric spaces. Int. J. Mod. Math., 4(3), pp. 285-301.

Boriceanu, M., Bota, M., & Petrusel, A. 2010. Multivalued fractals in b-metric spaces. Cent. Eur. J. Math., 8(2), pp. 367-377.

Bota, M., Molnar, A., & Varga, C. 2011. On Ekelandsvariational principle in b-metric spaces. Fixed Point Theory, 12(2), pp. 21-28.

Bakhtin, I.A. 1989. The contraction mapping principle in quasimetric spaces. Funct. Anal., Unianowsk Gos. Ped. Inst., 30, pp. 26-37.

Czerwik, S. 1993. Contraction mappings in b-metric spaces. Acta. Math. Inform. Univ. Ostraviensis, 1, pp. 5-11.

Czerwik, S. 1998. Nonlinear set-valued contraction mappings in b-metric spaces. Atti. Sem. Mat. Fis. Univ. Modena, 46, pp. 263-276.

Guo, D., & Lakshmikantham, V. 1987. Coupled fixed points of nonlinear operators with applications. Nonlinear Anal., 11, pp. 623-632.

Hussain, N., Abbas, M., Azam, A., & Ahmad, J. 2014. Coupled coincidence point results for a generalized compatible pair with applications. Fixed Point Theory and Applications, 62.

Hussain, N., & Shah, M.H. 2011. KKM mapping in cone b-metric spaces. Comput. Math. Appl., 62, pp. 1677-1684.

Huang, H., Paunović, Lj., & Radenović, S. 2015. On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces. J. Nonlinear Sci. Appl., 8, pp. 800-807.

Luong, N.V., & Thuan, N.X. 2011. Coupled fixed point in partially ordered metric spaces and applications. Nonlinear Anal., 74, pp. 983-992.

Mustafa, Z., Roshan, J.R., Parvaneh, V., & Kadelburg, Z. 2013. Some common fixed point results in ordered partial b-metric spaces. J. Inequal. Appl., 562.

Mustafa, Z., Roshan, J.R., Parvaneh, V., & Kadelburg, Z. 2014. Fixed point theorems for Weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces. J. Inequal. Appl., 46.

Mustafa, Z., Jaradat, M.M.M., Ansari, A.H., Popović, B.Z., & Jaradat, H.M. 2016. C-class functions with new approach on coincidence point results for generalized [Formula: see text]-weakly contractions in ordered b-metric spaces. Springerplus, 5(1), p. 802. pmid:27390643

Nieto, J.J., & Rodríguez-López, R. 2005. Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations. Order, 22(3), pp. 223-239. doi:10.1007/s11083-005-9018-5

Nieto, J.J., & Rodríguez-López, R. 2007. Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations. Acta Mathematica Sinica, English Series, 23(12), pp. 2205-2212. doi:10.1007/s10114-005-0769-0

Olatinwo, M.O. 2008. Some results on multi-valued weakly jungck mappings in b-metric space. Central European Journal of Mathematics, 6(4), pp. 610-621. doi:10.2478/s11533-008-0047-3

Wu, Y. 2008. New fixed point theorems and applications of mixed monotone operator. J. Math. Anal. Appl., 341, pp. 883-893.

Original Scientific Paper