In this work, we recall definition of functions
called as C-class and use the
concepts of dislocated metric, b-dislocated metric, altering distance function.
We prove some coincidence, fixed and common fixed point results for two pairs
of weakly compatible mappings under-contractive conditions and contractive conditions
depended on another function T. Our
theorems extend and generalize related results in the literature.
Cite this paper
Dine, J. , Zoto, K. and Ansari, A. H. (2018). Fixed Point Results of Contractive Mappings by Altering Distances and C-Class Functions in b-Dislocated Metric Spaces. Open Access Library Journal, 5, e4657. doi: http://dx.doi.org/10.4236/oalib.1104657.
Aage, C.T. and Salunke, J.N. (2008) Some Results of Fixed Point Theorem in Dislocated Quasi-Metric Spaces. Bulletin of Marathwada Mathematical Society, 9, 1-5.
Jungck, G. (1986) Compatible Mappings and Common Fixed Points. International Journal of Mathematics and Mathematical Sciences, 9, 771-779. https://doi.org/10.1155/S0161171286000935
Shrivastava, R., Ansari, Z.K. and Sharma, M. (2012) Some Results on Fixed Points in Dislocated and Dislocated Quasi-Metric Spaces. Journal of Advanced Studies in Topology, 3, 25-31.
Kutbi, M.A., Arshad, M., Ahmad, J. and Azam, A. (2014) Generalized Common Fixed Point Results with Applications. Abstract and Applied Analysis, 2014, Article ID: 363925.
Aydi, H., Vetro, C., Sintunavarat, W. and Kumam, P. (2012) Coincidence and Fixed Points for Contractions and Cyclical Contractions in Partial Metric Spaces. Fixed Point Theory and Applications, 2012, 124.
Ciric, L.B. (1974) A Generalization of Banach’s Contraction Principle. Proceedings of the American Mathematical Society, 45, 267-273. https://doi.org/10.2307/2040075
Das, K.M. and Naik, K.V. (1979) Common Fixed Point Theorems for Commuting Maps on Metric Spaces. Proceedings of the American Mathematical Society, 77, 369-373.
Arshad, M., Shoaib, A. and Beg, I. (2013) Fixed Point of a Pair of Contractive Dominated Mappings on a Closed Ball in an Ordered Dislocated Metric Space. Fixed Point Theory and Applications, 2013, 115. https://doi.org/10.1186/1687-1812-2013-115
Hussain, N., Roshan, J.R., Parvaneh, V. and Abbas, M. (2013) Common Fixed Point Results for Weak Contractive Mappings in Ordered b-Dislocated Metric Spaces with Applications. Journal of Inequalities and Applications, 2013, 486.
Khan, M.S., Swaleh, M. and Sessa, S. (1984) Fixed Points Theorems by Altering Distances between the Points. Bulletin of the Australian Mathematical Society, 30, 1-9. https://doi.org/10.1017/S0004972700001659
Popa, V. and Mocanu, M. (2009) Altering Distances and Common Fixed Points under Implicit Relations. Hacettepe Journal of Mathematics and Statistics, 38, 329-337.
Sastri, K.P. and Babu, G.V.R. (1998) Fixed Point Theorems in Metric Spaces by Altering Distance. Bulletin of the Calcutta Mathematical Society, 90, 175-182.
Sastri, K.P. and Babu, G.V.R. (1999) Some Fixed Point Theorems by Altering Distances between Two Points. Indian Journal of Pure and Applied Mathematics, 30, 641-647.
Babu, G.V.R., Nageswara Rao, K. and Alemayehu, G.N. (2010) Common Fixed Points of Two Pair of Generalized Weakly Contractive Maps. Advanced Studies in Contemporary Mathematics, 20, 575-594.
Babu, G.V.R. and Alemayehu, G.N. (2010) Point of Coincidence and Common Fixed Points of a Pair of Generalized Weakly Contractive Maps. Journal of Advanced Research in Pure Mathematics, 2, 89-106. https://doi.org/10.5373/jarpm.338.010810
Choudhury, B.S., Konar, P., Rhoades, B.E. and Metiya, N. (2011) Fixed Point Theorems for Generalized Weak Contractive Mappings. Nonlinerar Analysis, 74, 2116-2126. https://doi.org/10.1016/j.na.2010.11.017
Ansari, A.H. (2014) Note on (ψ, φ)-Contractive Type Mappings and Related Fixed Point. The 2nd Regional Conference on Mathematics and Applications, Tehran, September 2014, 377-380.
Hoxha, E., Ansari, A.H. and Zoto, K. (2014) Some Common Fixed Point Results through Generalized Altering Distances on Dislocated Metric Spaces. Proceedings of the 3rd Electronic International Interdisciplinary Conference, Zilina, 1-5 September 2014, 403-409.
Karapinar, E. and Salimi, P. (2013) Dislocated Metric Space to Metric Spaces with Some Fixed Point Theorems. Fixed Point Theory and Applications, 2013, 222. https://doi.org/10.1186/1687-1812-2013-222
Doric, D. (2009) Common Fixed Point for Generalized (ψ, φ)—Weak Contractions. Applied Mathematics Letters, 22, 1896-1900. https://doi.org/10.1016/j.aml.2009.08.001
Dutta, P.N. and Choudhury, B.S. (2008) A Generalisation of Contraction Principle in Metric Spaces. Fixed Point Theory and Applications, 2008, Article ID: 406368. https://doi.org/10.1155/2008/406368
Kumari, P.S. (2012) Common Fixed Point Theorems on Weakly Compatible Maps on Dislocated Metric Spaces. Mathematical Sciences, 6, 71. https://doi.org/10.1186/2251-7456-6-71
He, F. (2015) Common Fixed Point of Four Self Maps on Dislocated Metric Spaces. Journal of Nonlinear Sciences and Applications, 8, 301-308. https://doi.org/10.22436/jnsa.008.04.02
Bennani, S., Bourijal, H., El Moutawakil, D. and Mhanna, S. (2015) Some Common Fixed Point Theorems in Dislo-cated Metric Spaces. Journal of Nonlinear Sciences and Applications, 8, 86-92. https://doi.org/10.22436/jnsa.008.02.01
An, T.V., Chi, K.P., Karap?na-rand, E. and Thanh, T.D. (2012) An Extension of Generalized ψ, ?-Weak Contractions. International Journal of Mathematics and Mathematical Sciences, 2012, Article ID: 431872. https://doi.org/10.1155/2012/431872
Mustafa, Z., Roshan, J.R., Parvaneh, V. and Kadelburg, Z. (2013) Some Common Fixed Point Results in Ordered b-Metric Spaces. Journal of inequalities and Applications, 2013, 562.
Moradi, S. and Omid, M. (2010) A Fixed-Point Theorem for Integral Type Inequality Depending on Another Function. International Journal of Mathematical Analysis, 4, 1491-1499.