### A Common Fixed Point Theorem in Cone Metric Spaces over Banach Algebras

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Abbas, M. and G.Jungck (2008). Common fixed point results for non commuting mappings without continuity in cone metric spaces. J. Math. Anal.Appl. 341, 416–420.

Aliprantis, C.D. and R. Tourky (2007). Cones and duality, in :Graduate Studies in Mathematics. American Mathematicsl Society, Providence, Rhode Island.

Çkallı, H., A. Sönmez and Ç. Genç (2012). On an equivalence of topological vector space valued cone metric spaces and metric spaces. Appl. Math. Lett. 25, 429–433.

Dordević, M., D. Dorić, Z. Kadelburg, S. Radenovi and D. Spasić (2011). Fixed point results under c-distance in

tvs-cone metric spaces. Fixed Point Theory Appl. 2011, 9 pages.

Du, W.S. (2010). A note on cone metric fixed point theory and its equivalence. Nonlinear Anal. 72(5), 2259–2261.

Feng, Y. and W. Mao (2010). The equivalence of cone metric spaces and metric spaces. Fixed Point Theory 11(2), 259–264.

Huang, H. and S. Radenović (2015). Common fixed point theorems of generalized lipschitz mappings in cone b-metric spaces over Banach algebras and applications. J. Nonlinear Sci. Appl. 8(5), 787–799.

Huang, H., S. Radenović and G. Deng (2016). Some fixed point results of generalized lipschitz mappings on cone

b-metric spaces over Banach algebras. J. Comput. Anal. Appl. 20(3), 566–583.

Huang, H., S. Radenović and G. Deng (2017). A sharp generalization on cone b-metric space over banach algebra. J. Nonlinear Sci. Appl. 10(2), 429–435.

Huang, L.G. and X. Zhang (2007). Cone metric spaces and fixed point theorems of contractive mappings. J. Math.

Anal. Appl. 332(2), 1468–1476.

Janković, S., Z. Golubović and S. Radenović (2010). Compatible and weakly compatible mappings in cone metric spaces. Math. Comput. Model. 52, 1728–1738.

Janković, S., Z. Kadelburg and S. Radenović (2011). On cone metric spaces, a survey. Nonlinear Anal. TMA 74, 2591– 2601.

Jungck, G., S. Radenović, S. Radojević and V. Rakocević (2009). Common fixed point theorems for weakly compatible pairs on cone metric spaces. Fixed Point Theory and Applications 57, article ID 643840, 13 pages.

Kadelburg, Z., S. Radenović and V. Rakocević (2011). A note on the equivalence of some metric and cone metric fixed point results. Appl. Math. Lett. 24, 370–374.

Kantorovich, L.V. (1957). On some further applications of the newton approximation method. Vestn. Leningr. Univ. Ser. Mat. Mekah. Astron. 12(7), 68–103.

Khan, M.S., S. Shukla and S.M. Kang (2015). Fixed point theorems of weakly monotone presˇic´ mappings in ordered cone metric spaces. Bull. Korean Math. Soc. 52(3), 881–893.

Liu, H. and S. Xu (2013). Cone metric spaces over Banach algebras and fixed point theorems of generalized Lipschitz mappings. Fixed Point Theory Appl. 2013, 10 pages.

Malhotra, S.K., S. Shukla and R. Sen (2012). Some coincidence and common fixed point theorems in cone metric spaces. Bull. Math. Anal. Appl. 4(2), 64–71.

Radenović, Stojan (2009). Common fixed points under contractive conditions in cone metric spaces. Comput. Math.

Appl. 58, 1273–1278.

Rangamma, M. and K. Prudhvi (2012). Common fixed points under contractive conditions for three maps in cone metric spaces. Bulletin of Mathematical Analysis and Applications 4(1), 174–180.

Rezapour, Sh. and R. Hamlbarani (2008). Some notes on the paper cone metric spaces and fixed point theorems of contractive mappings. Math. Anal. Appl. 345, 719–724.

Vandergraft, J. S. (1967). Newton’s method for convex operators in partially ordered spaces. SIAM J. Numer. Anal.

, 406–432.

Vetro, P. (2007). Common fixed points in cone metric spaces. Rendiconti Del Circolo Mathematico Di Palermo pp. 464–468.

Zabre ǐko, P.P. (1997). K-metric and k-normed spaces: survey. Collect. Math.

### Refbacks

- There are currently no refbacks.