Presented at the 3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences) (ISAS2019-ENS), Ankara, Turkey, Apr 19, 2019

SETSCI Conference Proceedings, 2019, 4, Page (s): 333-342 , https://doi.org/

Published Date: 01 June 2019    | 709     16

Very recently orthogonal cone metric spaces, orthogonal completeness and orthogonal continuity are described and fixed points of orthogonal contractions are investigated by Bilgili Gungor [4]. In this paper, some generalizations of fixed point theorems in [4] are presented.

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[1] Abbas, M. and Jungck, G. (2008). Common fixed point results for noncommuting mappings without continuity in cone metric spaces. Journal of Mathematical Analysis and Applications, 341(1), 416-420.

[2] Abbas, M. and Rhoades, B. E. (2009). Fixed and periodic point results in cone metric spaces. Applied Mathematics Letters, 22(4), 511-515.

[3] Baghani, H., Gordji, M. E. and Ramezani, M. (2016). Orthogonal sets: The axiom of choice and proof of a fixed point theorem. Journal of Fixed Point Theory and Applications, 18(3), 465-477.

[4] Bilgili Gungor, N., Orthogonal cone metric spaces and fixed points of orthogonal contractions. Journal of Fixed Point Theory and Applications (In review)

[5] Gordji, M. E., Ramezani, M., De La Sen, M. and Cho, Y. J. (2017). On orthogonal sets and Banach fixed point theorem. Fixed Point Theory, 18(2), 569-578.

[6] Eshaghi Gordji, M. and Habibi, H. (2017). Fixed point theory in generalized orthogonal metric space. Journal of Linear and Topological Algebra (JLTA), 6(3), 251-260.

[7] Huang, L. G. and Zhang, X. (2007). Cone metric spaces and fixed point theorems of contractive mappings. Journal of mathematical Analysis and Applications, 332(2), 1468-1476.

[8] Ilic, D. and Rakocevic, V. (2008). Common fixed points for maps on cone metric space. Journal of Mathematical Analysis and Applications, 341(2), 876-882.

[9] Jankovi, S., Kadelburg, Z. and Radenovi, S. (2011). On cone metric spaces: a survey. Nonlinear Analysis: Theory, Methods and Applications, 74(7), 2591-2601.

[10] Ramezani, M. (2015). Orthogonal metric space and convex contractions. Int. J. Nonlinear Anal. Appl, 6(2), 127-132.

[11] Ramezani, M. and Baghani, H. (2017). Contractive gauge functions in strongly orthogonal metric spaces. Int. J. Nonlinear Anal. Appl, 8(2), 23-28.

[12] Rezapour, S. and Hamlbarani, R. (2008). 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.

[13] Turkoglu, D.and Abuloha, M. (2010). Cone metric spaces and fixed point theorems in diametrically contractive mappings. Acta mathematica sinica, English series, 26(3), 489-496.

[14] Vetro, P. (2007). Common fixed points in cone metric spaces. Rendiconti del circolo Matematico di Palermo, 56(3), 464-468.