Geodesic
Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces
Roshan, Jamal Rezaei1 ; Parvaneh, Vahid2 ; Kadelburg, Zoran3
1 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
3 Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia
Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 4, p. 229-245.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.007.04.01
Classification : 47H10, 54H25
Keywords: Common xed point, b-metric space, partially ordered set, weakly isotone increasing mappings.

Roshan, Jamal Rezaei 1 ; Parvaneh, Vahid 2 ; Kadelburg, Zoran 3

1 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
3 Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia 
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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 its applications, Tome 7 (2014) no. 4, p. 229-245. doi : 10.22436/jnsa.007.04.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.04.01/

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

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

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

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

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

[6] Altun, I.; H. Simsek Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., Article ID 621492, Volume 2010 (2010), pp. 1-17

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

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

[9] Ćirić, L.; Cakić, N.; Rajović, M.; J. S. Ume Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., Article ID 131294, Volume 2008 (2008), pp. 1-11

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

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

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

[13] Hussain, N.; Parvaneh, V.; Roshan, J. R.; Kadelburg, Z. Fixed points of cyclic ( \(\psi,\varphi,L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., Volume 2013:256 (2013), pp. 1-18

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

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

[16] Jovanović, M.; Kadelburg, Z.; Radenović, S. Common fixed point results in metric-type spaces, Fixed Point Theory Appl., Article ID 978121, Volume 2010 (2010), pp. 1-15

[17] M. A. Khamsi Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., Article ID 315398, Volume 2010 (2010), pp. 1-7

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

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

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

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

[22] Nieto, J. J.; Rodríguez-Lépez, R. Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica (Engl. Ser.), Volume 23 (2007), pp. 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), pp. 125-137

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

[25] Roshan, J. R.; Parvaneh, V.; Sedghi, S.; Shobkolaei, N.; W. Shatanawi Common fixed points of almost generalized \((\psi,\varphi)_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., Volume 2013:159 (2013), pp. 1-23

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

[27] Stanić, M. P.; Cvetković, A. S.; Simić, Su.; S. Dimitrijević Common fixed point under contractive condition of Ćirić's type on cone metric type space, Fixed Point Theory Appl., Volume 2012:35 (2012), pp. 1-7

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