On some alpha-admissible contraction mappings on Branciari b-metric spaces

Year 2017, Volume: 1 Issue: 1, 1 - 13, 30.09.2017

Selma Gülyaz-özyurt

https://doi.org/10.31197/atnaa.318445

Cited By: 17

Abstract

In this paper α-admissible contraction mappings on Branciari b-metric spaces are defined. Conditions for the existence and uniqueness of fixed points for these mappings are discussed and related theorems are proved. Various consequences of these theorems are given and specific examples are presented.

Keywords

Fixed point, Branciari b-metric space, α-admissible contraction mappings, b-comparison functions

References

• [1] H. Aydi, E. Karapınar, D. Zhang, On common fixed points in the context of Brianciari metric spaces, Results Math, vol.71, 73-92, (2017).
• [2] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Functional Analysis, vol. 30, 26–37, (1989).
• [3] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized matric spaces, Publ. Math. Debrecen, vol.7(1-2), 31-37, (2000).
• [4] V. Berinde, Contrac¸tii Generalizate ¸si Aplica¸tii, Editura Cub Press, vol. 2 , Baia Mare, Romania, (1997).
• [5] V. Berinde, Sequences of operators and fixed points in quasi-metric spaces, Mathematica, vol. 41, 23-27, (1997). 1
• [6] V. Berinde, Generalized contractions in quasimetric spaces, in Seminar on Fixed Point Theory, vol. 93 of Preprint 3, Babe¸s-Bolyai University, Cluj-Napoca, Romania, 3-9, (1993).
• [7] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., vol. 1, 5–11, (1993).
• [8] R. George, S. Radenovic, K.P. Reshma, S. Shukla, Rectangular b-metric spaces and contraction principle, J. Nonlinear Sci. Appl., vol. 8, 1005–1013, (2015).
• [9] E. Karapınar, B, Samet, Generalized α-ψ contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, vol.2012, Article ID:793486, (2012).
• [10] W. A. Kirk, N. Shahzad, Generalized metrics and Caristis theorem. Fixed Point Theory Appl. 2013, Article ID 129 (2013).
• [11] I. A. Rus., Generalized contractions and applications, Cluj University Press, Cluj-Napoca, Romania, (2001). 1, 1.8
• [12] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis, vol.75, 2154-2165, (2012).