Open Access

Ortogonal Koni Metrik Uzaylarda Bazı Ortak Sabit Nokta Teoremleri

Mehmet  SÜRMELİOĞLU  1, Nurcan  BİLGİLİ GÜNGÖR  2*
1Amasya Üniversitesi  , Amasya , Türkiye
2Amasya Üniversitesi  , Amasya , Türkiye
* Corresponding author: bilgilinurcan@gmail.com

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): 326-332

Published Date: 01 June 2019

2017 yılında Gordji, Ramazani, De La Sen ve Cho [1] ortogonal küme ve ortogonal metrik uzay kavramlarını vermişlerdir. Ardından genelleştirilmiş metrik uzaylarda sabit nokta çalışmaları yapılmıştır ([2]). 2018 yılında Bilgili Gungor [3], koni metrik uzaylarda ortogonallik bağıntısını kullanarak büzülme dönüşümleri için sabit noktaların varlığını ispatlamıştır. Bu çalışmada ise Bilgili Gungor [3], Abbas ve Jungck [4] çalışmalarından esinlenerek, ortogonal koni metrik uzaylarda tanımlı öz dönüşümler için uygun büzülme şartları kullanılarak, ortak sabit noktaların varlığı ve tekliği incelenmiştir.

Keywords - Ortogonal küme, metrik uzay, koni metrik uzay, büzülme dönüşümleri, sabit nokta, ortak sabit nokta

[1] 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.

[2] 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.

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

[4] 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.

[5] Jungck, G., Commuting mappings and fixed points. The American Mathematical Monthly, 83(4), 261-263, 1976.

[6] Sessa, S., On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math, 32(46), 149-153, 1982.

[7] G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (4), 771–779, 1986.

[8] Pant, R. P., Common fixed points of noncommuting mappings. Journal of Mathematical Analysis and Applications, 188(2), 436-440, 1994.

[9] Kannan, R, Some results on fixed points. Bull. Cal. Math. Soc., 60, 71- 76, 1968.

[10] G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. (FJMS) 4,199–215, 1996.

[11] G. Jungck, B.E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (3), 227–238, 1998.

[12] 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.

[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.

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