Fixed point results with $c_A$ distance in cone A-metric spaces

Yıl 2025, Cilt: 8 Sayı: 2, 120 - 132, 19.10.2025

Nurcan Bilgili Güngör , Buse Elif Uluçınar

Öz

In this paper, the concept of a $c_A$-distance in a cone A-metric space with some illustrative examples is presented. Then, some common fixed point theorems for weakly
compatible self mappings are gotten by using this new distance. Also, some common fixed point results in cone A-metric spaces for
weakly compatible self mappings are held without assumption of the normality for cones.

Anahtar Kelimeler

fixed point , c_a distance , A-metric space , weakly compatible mapping

Kaynakça

• Abbas, M., & 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.
• Abbas, M., & Rhoades, B. E. (2009). Fixed and periodic point results in cone metric spaces. Applied Mathematics Letters, 22 (4), 511–515.
• Abbas, M., Ali, B., & Suleiman, Y. I. (2015). Generalized coupled common fixed point results in partially ordered A-metric spaces. Fixed Point Theory and Applications, 2015, 1–24.
• Singh, K. A., & Singh, M. R. (2018). Some fixed point theorems of cone Sb-metric space. Journal of the Indian Academy of Mathematics, 40, 255–272.
• Singh, K. A., & Singh, M. R. (2020). Some coupled fixed point theorems in cone Sb-metric space. Journal of Mathematics and Computer Science, 10, 891–905.
• Aghajani, A., Abbas, M., & Roshan, J. R. (2014). Common fixed point of generalized weak contractile mappings in partially ordered Gb-metric spaces. Filomat, 28 (6), 1087–1101. https://doi.org/10. 2298/FIL1406087A
• Aleksić, S., Kadelburg, Z., Mitrović, Z. D., & Radenović, S. (2018). A new survey: Cone metric spaces. arXiv. https://arxiv.org/abs/1805.04795
• Bakhtin, I. A. (1989). The contraction mapping principle in almost metric spaces. Funct. Anal., Gos. Ped. Inst. Unianow’sk, 30, 26–37.
• Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3 (1), 133–181.
• Czerwik, S. (1993). Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, 1, 5–11.
• Czerwik, S. (1998). Nonlinear set-valued contraction mappings in b-metric spaces. Atti del Seminario Matematico e Fisico dell’Università di Modena, 46 (2), 263–276.
• Dhage, B. C. (1984). A study of some fixed point theorem [Ph.D. thesis, Marathwada University].
• Dhage, B. C. (2000). Generalized metric spaces and topological structure. I. Analele Ştiinţifice ale Universităţii "Al. I. Cuza" din Iaşi, Matematică, 46, 3–24.
• Dhamodharan, D., & Krishnakumar, R. (2017). Cone S-metric space and fixed point theorems of contractive mappings. Annals of Pure and Applied Mathematics, 14 (2), 237–243.
• Dung, N. V., Hieu, N. Y., & Radojevic, S. (2014). Fixed point theorems for ψ-monotone maps on partially ordered S-metric spaces. Filomat, 28 (9), 1885–1898. https://doi.org/10.2298/FIL1409885D
• Fadail, Z. M., Savić, A., & Radenović, S. (2022). New distance in cone S-metric spaces and common fixed point theorems. Journal of Mathematics and Computer Science, 26 (4), 368–378.
• Fernandez, J., Saelee, S., Saxena, K., Malviya, N., & Kumam, P. (2017). The A-cone metric space over Banach algebra with applications. Cogent Mathematics, 4 (1), Article 1282690.
• Huang, L. G., & Zhang, X. (2007). Cone metric spaces and fixed point theorems of contractive mappings. Journal of Mathematical Analysis and Applications, 332 (2), 1468–1476.
• Ilić, D., & Rakočević, V. (2008). Common fixed points for maps on cone metric space. Journal of Mathematical Analysis and Applications, 341 (2), 876–882.
• Janković, S., Kadelburg, Z., & Radenović, S. (2011). On cone metric spaces: A survey. Nonlinear Analysis: Theory, Methods and Applications, 74 (7), 2591–2601.
• Jungck, G., Radenović, S., Radojević, S., & Rakočević, V. (2009). Common fixed point theorems for weakly compatible pairs on cone metric spaces. Fixed Point Theory and Applications, 2009, 1–13.
• Matthews, S. G. (1994). Partial metric topology. In Proceedings of the 8th Summer Conference on General Topology and Applications. Annals of the New York Academy of Sciences, 728, 183–197.
• Mustafa, Z., & Sims, B. (2003). Some results concerning D-metric spaces. In Proceedings of the International Conference on Fixed Point Theory and Applications (pp. 189–198). Valencia, Spain.
• Mustafa, Z., Sims, B. (2006). A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis, 7 (2), 289–297.
• Naidu, S. V. R., Rao, K. P. R., & Srinivasa, N. (2004). On the topology of D-metric spaces and the generation of D-metric spaces from metric spaces. International Journal of Mathematics and Mathematical Sciences, 2004 (51), 2719–2740.
• Naidu, S. V. R., Rao, K. P. R., & Srinivasa, N. (2005). On the concepts of balls in a D-metric space. International Journal of Mathematics and Mathematical Sciences, 2005 (1), 133–141.
• Souayak, N., & Mlaiki, N. (2016). A fixed point theorem in S-metric spaces. Journal of Mathematics and Computer Science, 16, 131–139.
• Rezapour, S., & 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.
• Saluja, G. S. (2020). Fixed point theorems on cone S-metric spaces using implicit relation. Cubo (Temuco), 22 (2), 273–289.
• Saluja, G. S. (2021). Some fixed point results under contractive type mappings in cone Sb-metric spaces. Palestine Journal of Mathematics, 10, 547–561.
• Sedghi, S., Rao, K. P. R., & Shobe, N. (2007). Common fixed point theorems for six weakly compatible mappings in D∗-metric spaces. International Journal of Mathematics and Mathematical Sciences, 2007 (6), 225–237.
• Sedghi, S., Shobe, N., & Zhou, H. (2007). A common fixed point theorem in D∗-metric spaces. Fixed Point Theory and Applications, 2007 (13), Article 27906.
• Sedghi, S., Shobe, N., & Aliouche, A. (2012). A generalization of fixed point theorem in S-metric spaces. Matematički Vesnik, 64, 258–266.