Fixed Point Results for Multivalued Operators On b_2 Metric Spaces

The aim of this paper is to establish fixed point theorem for multivalued operators in b_2-metric space and generalize the results of Chifu and Petruel (2017) and Sheng, Ren and Zhong (2018). Moreover, we present an example for the main results. The aim of this paper is to establish fixed point theorem for multivalued operators in b_2-metric space and generalize the results of Chifu and Petruel (2017) and Sheng, Ren and Zhong (2018). Moreover, we present an example for the main results.The aim of this paper is to establish fixed point theorem for multivalued operators in b_2-metric space and generalize the results of Chifu and Petruel (2017) and Sheng, Ren and Zhong (2018). Moreover, we present an example for the main results.

Anahtar Kelimeler:

Fixed point, b_2 metric space, Mathematics

?? Metrik Uzayında Çok Değişkenli Operatörler için Sabit Nokta Sonuçları Üzerine

Bu çalışmanın amacı, ?2 -metrik uzayında çok değişkenli operatörler için sabit nokta teoremi oluşturmak ve Chifu ve Petruşel (2017) ve Yihao, Ren ve Zhong (2018) sonuçlarını genelleştirmektir. Ayrıca, ana teoremi göstermek için bir örnek verilmiştir. Bu çalışmanın amacı, ?2 -metrik uzayında çok değişkenli operatörler için sabit nokta teoremi oluşturmak ve Chifu ve Petruşel (2017) ve Yihao, Ren ve Zhong (2018) sonuçlarını genelleştirmektir. Ayrıca, ana teoremi göstermek için bir örnek verilmiştir.

Keywords:

Hardy-Rogers daralmaları, çok değişkenli operatörler, ?2 metrik uzayı,

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[1] Aliouche, A. and Simpson, C. 2012. “Fixed point and Lines in 2-Metric Spaces”, Advanced in Mathematics, 229, 668–690.
[2] Bakhtin, I.A. 1989. “The contraction mapping principle in quasimetric spaces”, Funct. Anal. Unianowsk Gos. Ped. Inst., 30,.26–37.
[3] Banach, S. 1922. “Sur les oprations dans les ensembles abstraits et leurs applications”, Fund. Math 3, 133–181.
[4] Chifu, C. and Petruel, G. 2017. “Fixed Point results for multivalued Hardy- Rogers Constractions in bMetric Spaces”, Filomat, 31(8), 2499–2507.
[5] Cui, J., Zhao J. and Zhong L. 2017. “Unique common fixed point in b2 metric spaces”, Open Access Library Journal, 4, 1–8.
[6] Czerwik, S. 1993. “Contraction mappings in b-metric spaces”, Acta Math. Inf. Univ. Ostraviensis, 1, 5–11.
[7] Demma, M., Saadati,R. and Vetro, P. 2016. “Fixed Point results on b-metric space via picard sequences and b-simulation functions”, Iran J. Math. Sci. Inform, 11(1), 123–136.
[8] Dung, N.V. and Le Hang, V.T. 2013. “Fixed point theorems for weak C-contractions in Partiallyordered 2-Metric spaces”, Fixed Point Theory and Applications, 161, 2013.
[9] Fadail, Z.M., Ahmad, A.G.B. and Ozturk, V. et. al. 2015. “Some Remarks on Fixed Point Results of b-2 metric spaces”, Far East Journal of Mathematical Sciences, 97, 533–548.
[10] Gahler, V.S. 1963. “2-metrische Ra¨ume und ihre topologische Struktur”, Mathematische Nachrichten, 26, 115–118.
[11] Hardy, G. E. and Rogers, A. D. 1973. “A generalization of fixed point theorem of Reich”, Canad. Math. Bull., 16, 201–208.
[12] Mustafa, Z., Parvane, V., Roshan, J. R. and Kadelburg, Z. 2014. “b-2 metric spaces and some fixed point theorems”, Fixed Point Theory and Applications, 144.
[13] Piao, Y. J. 2013. “Common fixed points for two mappings satisfying some expansive conditions on 2-metric spaces”, Journal of systems Science and Mathematical Sciences, 33, 1370–1379.
[14] Sheng, Y., Ren, J. and Zhong, L. 2018. “Unique common fixed points for mappings Satisfying φ-Contractions on b2 Metric Spaces”, Open Access Library Journal, 5, e4723.
[15] Suzuki, A. 2018. Generalization of Hegeu¨s-Szila´gyi’s, “Fixed Point Theorem in Complete Metric Spaces”, Fixed Point Theorem and Applications, 1, 1–10.