Study the topology of Branciari metric space via the structure proposed by Csaszar

Year 2017, Volume: 1 Issue: 1, 48 - 56, 30.09.2017

Dong Zhang

https://doi.org/10.31197/atnaa.379113

Cited By: 1

Abstract

In this paper, we topologically study the generalized metric space proposed by Branciari [3] via the weak structure proposed by Cs´asz´ar [9, 10], and compare convergent sequences in several different senses. We also introduce the concepts of available points and unavailable points on such structures. Besides, we define the continuous function on structures and investigate further characterizations of continuous functions.

Keywords

Branciari metric space, generalized topology, structure

References

• H. Aydi, E. Karapınar, B. Samet, Fixed points for generalized (α,ψ)-contractions on generalized metric spaces, J. Ineq. Appl., 2014(2014), Article ID 229.
• H. Aydi, E. Karapınar, and D. Zhang, On common xed points in the context of Brianciari metric spaces, Results in Mathematics, 71 (2017), 73-92.
• A. Branciari, A xed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen., 57 (2000), 31-37.
• N. Bilgili, E. Karapnar, A note on \common xed points for ( ; ; )-weakly contractive mappings in generalized metric spaces", Fixed Point Theory Appl., 2013 (2013), Article ID 287.
• W.A. Kirk, N. Shahzad, Generalized metrics and Caristi's theorem, Fixed Point Theory Appl., 2013 (2013), Article ID 129.
• C. Li and D.Zhang, On generalized metric spaces and generalized convex contractions, Fixed point theory (accepted)
• Selma Gulyaz Ozyurt, On some -admissible contraction mappings on Branciari b-metric spaces, Adv. Theory Nonlinear Anal. Appl. (2017) 1-13.
• Suzhen Han, Jianfeng Wu, Dong Zhang, Properties and principles on partial metric spaces, Topology Appl., 230 (2017), 77-98.
• A. Csaszar, Generalized topology, generized continuity, Acta Math. Hungar. (2002), 351-357.
• A. Csaszar, Weak structures, Acta Math. Hungar., 131 (2011), 193{195, doi: 10.1007/s10474-010-0020-z.
• E. Ekici, On weak structures due to Csaszar, Acta Math. Hungar., 134 (2012), 565-570, doi:10.1007/s10474-011-0145-8.
• M. Navaneethakrishnan and S. Thamaraiselvi, On weak structures of Csaszar, Acta Math. Hungar., 137 (3) (2012), 224-229, DOI: 10.1007/s10474-012-0218-3