Solution of nonlinear integral equations via fixed point theorems in Gmetric spaces

20141121 https://doi.org/10.14419/ijamr.v3i4.3651 
Common fixed point, partially ordered set, dominating maps. 
Abstract
The main aim of this paper is to prove that the existence and uniqueness of solutions for systems of simultaneous Volterra Â Hammerstein and Urysohn nonlinear integral equations in Gmetric spaces andÂ partially ordered Gmetric spaces settings Â by using common fixed point theorems satisfying generalized contractive conditions.

References
 M. Abbas , Y.J. Cho and T. Nazir, Common fixed points of Cirictype contractive mappings in two ordered generalized metric spaces, Fixed Point Theory and Appl., 2012, 139 (2012).
 M. Abbas, S. H. Khan and T. Nazir, Common fixed points of Rweakly commuting maps in generalized metric spaces, Fixed Point Theory Appl., 2011, 41 (2011).
 M. Abbas, T. Nazir, and S. RadenoviÄ‡, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24 (2011) 1520â€“1526.
 M. Abbas, T. Nazir, and R. Saadati, Common fixed point results for three maps in generalized metric space, Advances in Difference Equations, 2011, 49 (2011).
 R. P. Agarwal, M. A. ElGebeily and D. Ã’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008) 109â€“116.
 I. Cabrera, J. Harjani and K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara, 59, (2013), 251â€“258.
 L. Gholizadeh, A fixed point theorem in generalized ordered metric spaces with application, J. Nonlinear Sci. Appl., 6 (2013), 244â€“251.
 S. GÃ¼lyaz, E. Karapinar and V. RakoceviÄ‡ and P. Salimi, Existence of a solution of integral equations via fixed point theorem Journal of Inequalities and Appl., 2013, (2013), 16pages.
 J. Harjani, B. Lopez and K. Sadarangani, A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Abstr. Appl. Anal., 2010, (2010), 1â€“8.
 M. S. Khan, M. Swales and S. Sessa: Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), 1â€“9.
 Z. Mustafa, V. Parvaneh, M. Abbas, J. Roshan Some coincidence point results for generalized (Ïˆ , Ï†)weakly contractive mappings in ordered Gmetric spaces, Fixed Point Theory and Appl., 2013, 326 (2013).
 Z. Mustafa and B. Sims, Some remarks concerning Dmetric spaces, Intern. Conf. Fixed Point. Theory and Applications, Yokohama (2004), 189â€“198.
 Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Analysis, 7 (2006), 289â€“297.
 J. J. Nieto and R. RodrguezLÃ³pez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223â€“239.
 J. J. Nieto and R. RodrguezLÃ³pez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin., 23 (2007), 2205â€“2212.
 H. K. Pathak, Y. J. Cho and S. M. Kang, Common fixed points of type (A) and applications, Intern. J. Math. Math. Sci., 21 (1998), 681â€“694.
 H.K. Pathak, M.S. Khan, Z. Liu and J. S. Ume, Fixed point theorems in metrically convex spaces and applications J. Nonlinear Convex Anal., 4(2) (2003), 231â€“244.
 H. K. Pathak, M. S. Khan and R. Tiwari, A common fixed point theorem and its application to nonlinear integral equations Computers and Mathematics with Applications, 53 (2007), 961â€“971.
 H. K. Pathak, S. N. Mishra and A. K. Kalinde, Common fixed point theorems with applications to nonlinear integral equations, Demonstratio Math., XXXII (1999), 547â€“564.
 S. RadenoviÄ‡ and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Computers and Mathematics with Applications, 60 (2010), 1776â€“1783.
 A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc., 132 (2004), 1435â€“1443.
 K. P. R. Rao, K. B. Lakshmi and Z. Mustafa, A unique common fixed point theorem for six maps in Gmetric spaces, Int. J. Nonlinear Anal. Appl., 3 (1) (2012), 17â€“23.
 R. A. Rashwan and S. M. Saleh, Common fixed point theorems for six mappings in ordered Gmetric spaces, Advances in Fixed Point Theory, 3(1) (2013), 105â€“125.
 R. A. Rashwan and S. M. Saleh, A common fixed point theorem of three (Ïˆ , Ï†)weakly contractive mapping in Gmetric spaces, Ser. Math. Inform., 28(3) (2013), 323â€“334.
 W. Shatanawi and M. Postolache, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory and Appl., 2013, 271 (2013).
 W. Shatanawi, Some fixed point theorems in ordered Gmetric spaces and applications, Abstract and Applied Analysis, (2011), Article ID 126205, 11 pages.

Downloads
Additional Files

How to Cite
Rashwan, R., & Saleh, S. (2014). Solution of nonlinear integral equations via fixed point theorems in Gmetric spaces. International Journal of Applied Mathematical Research, 3(4), 561571. https://doi.org/10.14419/ijamr.v3i4.3651Received date: 20140927
Accepted date: 20141027
Published date: 20141121