Nurcan BİLGİLİ GÜNGÖR, Mehmet SÜRMELİOĞLU

SOME FIXED POINT THEOREMS FOR CONTRACTIVE MAPPINGS ON ORDERED ORTHOGONAL CONE METRIC SPACES

Very recently, orthogonal cone metric spaces, orthogonal completeness and orthogonal continuity are described in \cite{BG2019MS}. Also some fixed point theorems and their conclusions are proved on orthogonal cone metric spaces in there. In this paper, some fixed point theorems for contractive mappings are presented on ordered orthogonal cone metric spaces. Also an illustrative example is given.

Keywords:

contractive mapping, fixed point, cone metric space orthogonal cone metric space, ordered metric space,

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Abbas, M. and Jungck, G. , Common fixed point results for noncommuting mappings without continuity in cone metric spaces. Journal of Mathematical Analysis and Applications, 341(1), 416-420,(2008).
Abbas, M. and Rhoades, B. E., Fixed and periodic point results in cone metric spaces. Applied Mathematics Letters, 22(4), 511-515, 2009.
Baghani, H., Gordji, M. E. and Ramezani, M. , Orthogonal sets: The axiom of choice and proof of a fixed point theorem. Journal of Fixed Point Theory and Applications, 18(3), 465-477, 2016.
Bilgili Gungor, N. , Orthogonal cone metric spaces and fixed points of orthogonal contractions. Mathematical Sciences, 2019 .(In review)
Gordji, M. E., Ramezani, M., De La Sen, M. and Cho, Y. J., On orthogonal sets and Banach fixed point theorem. Fixed Point Theory, 18(2), 569-578, 2017.
Eshaghi Gordji, M. and Habibi, H., Fixed point theory in generalized orthogonal metric space. Journal of Linear and Topological Algebra (JLTA), 6(3), 251-260, 2017.
Huang, L. G. and Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings. Journal of mathematical Analysis and Applications, 332(2), 1468-1476, 2007.
Ilic, D. and Rakocevic, V., Common fixed points for maps on cone metric space. Journal of Mathematical Analysis and Applications, 341(2), 876-882, 2008.
Janković, S., Kadelburg, Z. and Radenović, S., On cone metric spaces: a survey. Nonlinear Analysis: Theory, Methods and Applications, 74(7), 2591-2601, 2011.
Ramezani, M. , Orthogonal metric space and convex contractions. Int. J. Nonlinear Anal. Appl, 6(2), 127-132, 2015.
Ramezani, M. and Baghani, H., Contractive gauge functions in strongly orthogonal metric spaces. Int. J. Nonlinear Anal. Appl, 8(2), 23-28, 2017.
Ran, A. C., and Reurings, M. C., A fixed point theorem in partially ordered sets and some applications to matrix equations. proceedings of the American Mathematical Society, 1435-1443, 2004.
Rezapour, S. and Hamlbarani, R., Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”. Journal of Mathematical Analysis and Applications, 345(2), 719-724, 2008.
Turkoglu, D.and Abuloha, M., Cone metric spaces and fixed point theorems in diametrically contractive mappings. Acta mathematica sinica, English series, 26(3), 489-496, 2010.
Vetro, P., Common fixed points in cone metric spaces. Rendiconti del circolo Matematico di Palermo, 56(3), 464-468, 2007.