Volume 21 | Number 1 | Year 2015 | Article Id. IJMTT-V21P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V21P508
In this paper we study a class of self-mappings on a Cone Banach Space which have at least one fixed point. More precisely for a closed and convex subset C of a cone Banach space with a generalized norm that satisfy a special condition. We are proposing some extensions of the results of Karapinar and idea Multu and Yolku using operator Φp.
[1] Rzepecki, B., ―On fixed point theorems of Maia type, Publications de l’Institut Mathematique, vol. 28_42_, pp. 179–186, 1980.
[2] Maia, M.G., ―Un’osservazione sulle contrazioni metriche, Rendiconti del Seminario Matematico della Universita di Padova, vol. 40, pp. 139–143, 1968.
[3] Lin, S. D., ― A common fixed point theorem in abstract space Indian Journal of Pure and Applied Mathematics. Vol. 18, n0.8, pp. 685-690.1987
[4] Huang L,-G., Zhang, X., ―Cone metric spaces and fixed point theorems of contractive mappings,Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 1468–1476, 2007
[5] Karapinar, E., Fixed point theorems in Cone Banach Spaces. Hindawi Publishing Company. Vol. 2009.Article ID 609281, 9 pages.
[6] Mutlu, A., Yolcu, N., Fixed point theorems for p operator in cone Banach space, Fixed point theory and Applications, 2013, 2013; 56
[7] Rezapour Sh., and Hamlbarani, R., ―Some notes on the paper: ―Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, vol. 345, no. 2, pp. 719–724, 2008.
[8] Turkoglu, D., Abuloha, M., and Abdeljawad, T., ―KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 1, pp. 348–353, 2010.
[9] Sahin I., Telci, M., ―Fixed points of contractive mappings on complete cone metric spaces, Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 1, pp. 59–67, 2009.
[10] Suzuki, T., ―Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, Journal of Mathematical Analysis and
Applications, vol. 340, no. 2, pp. 1088–1095, 2008. Fixed Point Theory and Applications 9 [11] Deimling, K., Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
[12] Abdeljawad T.,Karapinar, E., ―Quasicone Metric Spaces and Generalizations of Caristi Kirk’s Theorem, Fixed Point Theory and Applications, vol. 2009, p. 9 page, 2009.
Elvin Rada, Agron Tato, "An extension of a fixed point results with Φp operator in Cone Banach Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 21, no. 1, pp. 58-63, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V21P508