Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered *G*-Partial Metric Spaces

Affiliation(s)

Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria.

Department of Mathematics, Covenant University, Ota, Nigeria.

Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria.

Department of Mathematics, Covenant University, Ota, Nigeria.

ABSTRACT

We introduce the
concept of generalized quasi-contraction mappings in *G*-partial metric spaces and prove some fixed point results in
ordered *G*-partial metric spaces. The
results generalize and extend some recent results in literature.

KEYWORDS

Fixed Points, Generalized Quasi-Contraction Maps, Bounded Orbit, Partially Ordered Set,*G*-Partial Metric Spaces

Fixed Points, Generalized Quasi-Contraction Maps, Bounded Orbit, Partially Ordered Set,

Cite this paper

Olaleru, J. , Eke, K. and Olaoluwa, H. (2014) Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered*G*-Partial Metric Spaces. *Applied Mathematics*, **5**, 1004-1012. doi: 10.4236/am.2014.56095.

Olaleru, J. , Eke, K. and Olaoluwa, H. (2014) Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered

References

[1] Ciric, L.B. (1974) A Generalization of Banach’s Contraction Principle. Proceedings of the American Mathematical Society, 45, 267-273.

http://dx.doi.org/10.2307/2040075

[2] Ciric, L.B. (1971) Generalized Contractions and Fixed Point Theorems. Publications of the Institute of Mathematics, 12, 19-26.

[3] Wong, C.S. (1974) Generalized Contraction and Fixed Point Theorems. Proceedings of the American Mathematical Society, 42, 409-417.

http://dx.doi.org/10.1090/S0002-9939-1974-0331358-4

[4] Kiany, F. and Harandi, A.A. (2013) Fixed Point Theory for Generalized Ciric Quasi-Contraction Maps in Metric Spaces. Fixed Point Theory and Applications, 2013, 6 p.

[5] Rodriguez-Lopez, R. and Nieto, J.J. (2005) Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equation. A Journal on the Theory of Ordered Sets and Its Applications, 22, 223-239.

[6] Ran, A.C.M. and Reurings, M.C.B. (2003) A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations. Proceedings of the American Mathematical Society, 132, 1435-1443.

http://dx.doi.org/10.1090/S0002-9939-03-07220-4

[7] Matthews, S.G. (1992) Partial Metric Spaces. 8th British Colloquium for Theoretical Computer Science, Research Report 212, Dept. of Computer Science, University of Warwick, 708-718.

[8] Mustafa, Z. and Sims, B. (2006) A New Approach to Generalized Metric Spaces. Journal of Nonlinear and Convex Analysis, 7, 289-297.

[9] Gordji, M.E., Baghani, H. and Kim, G.H. (2012) A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations. Discrete Dynamics in Nature and Society, 2012, 981517.

[10] Saadati, R., Vaezpour, S.M., Vetro, P. and Rhoades, B.E. (2010) Fixed Point Theorems in Generalized Partially Ordered G-Metric Spaces. Mathematical and Computer Modelling, 852, 797-801.

http://dx.doi.org/10.1016/j.mcm.2010.05.009

[11] Turkoglu, D., Abuloha, M. and Abdejawad, T. (2011) Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces. Mathematical Communications, 16, 325-334.

[12] Sastry, K.P.R. and Naidu, S.V.R. (1980) Fixed Point Theorems for Generalized Contraction Mappings. Yokohama Mathematical Journal, 28, 15-29.

[1] Ciric, L.B. (1974) A Generalization of Banach’s Contraction Principle. Proceedings of the American Mathematical Society, 45, 267-273.

http://dx.doi.org/10.2307/2040075

[2] Ciric, L.B. (1971) Generalized Contractions and Fixed Point Theorems. Publications of the Institute of Mathematics, 12, 19-26.

[3] Wong, C.S. (1974) Generalized Contraction and Fixed Point Theorems. Proceedings of the American Mathematical Society, 42, 409-417.

http://dx.doi.org/10.1090/S0002-9939-1974-0331358-4

[4] Kiany, F. and Harandi, A.A. (2013) Fixed Point Theory for Generalized Ciric Quasi-Contraction Maps in Metric Spaces. Fixed Point Theory and Applications, 2013, 6 p.

[5] Rodriguez-Lopez, R. and Nieto, J.J. (2005) Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equation. A Journal on the Theory of Ordered Sets and Its Applications, 22, 223-239.

[6] Ran, A.C.M. and Reurings, M.C.B. (2003) A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations. Proceedings of the American Mathematical Society, 132, 1435-1443.

http://dx.doi.org/10.1090/S0002-9939-03-07220-4

[7] Matthews, S.G. (1992) Partial Metric Spaces. 8th British Colloquium for Theoretical Computer Science, Research Report 212, Dept. of Computer Science, University of Warwick, 708-718.

[8] Mustafa, Z. and Sims, B. (2006) A New Approach to Generalized Metric Spaces. Journal of Nonlinear and Convex Analysis, 7, 289-297.

[9] Gordji, M.E., Baghani, H. and Kim, G.H. (2012) A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations. Discrete Dynamics in Nature and Society, 2012, 981517.

[10] Saadati, R., Vaezpour, S.M., Vetro, P. and Rhoades, B.E. (2010) Fixed Point Theorems in Generalized Partially Ordered G-Metric Spaces. Mathematical and Computer Modelling, 852, 797-801.

http://dx.doi.org/10.1016/j.mcm.2010.05.009

[11] Turkoglu, D., Abuloha, M. and Abdejawad, T. (2011) Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces. Mathematical Communications, 16, 325-334.

[12] Sastry, K.P.R. and Naidu, S.V.R. (1980) Fixed Point Theorems for Generalized Contraction Mappings. Yokohama Mathematical Journal, 28, 15-29.