Geraghty type contraction mappings on Branciari b-metric spaces

Year 2017, Volume: 1 Issue: 2, 147 - 160, 20.12.2017

İnci M. Erhan

https://doi.org/10.31197/atnaa.379097

Abstract

In this paper fixed points of α-admissible contraction mappings of Geraghty type defined on Branciari bmetric spaces are studied. Existence and uniqueness theorems for these types of mappings of are proved. Some consequences of these theorems are given and specific examples are presented.

Keywords

fixed point, Branciari b-metric space, α-admissible contraction mappings, Geraghty contraction

References

• H. Aydi, E. Karapınar, D. Zhang, On common fixed points in the context of Brianciari metric spaces, Results Math, vol.71, 73-92, (2017).
• I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Functional Analysis, vol. 30, 26-37, (1989). 1 1.2
• A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized matric spaces, Publ. Math. Debrecen, Vol. 57, 31-37, (2000).
• S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., Vol. 1, 5U11, (1993).
• R. George, S. Radenovic, K. P. Reshma, S. Shukla, Rectangular b-metric spaces and contraction principle, J. Nonlinear Sci. Appl., Vol. 8, 1005U1013, (2015).
• M. Geraghty, On contractive mappings, Proceedings of American Math. Soc., vol. 40, 604-608, (1973).
• H. Huang, L. Paunovic and S. Radenovic, On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces, J. Nonlinear Science and Appl., vol.8, 800-807, (2015).
• N. Hussain, Z. Kadelburg, S. Radenovitc, F. Al-Solamy, Comparison functions and fixed point results in partial metric spaces, Abstract and Applied Analysis, vol. 2012, Article ID 605781, 15 pages, (2012).
• E. Karapınar, B. Samet, Generalized - contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, vol.2012, Article ID:793486, (2012).
• W. A. Kirk, N. Shahzad, Generalized metrics and CaristiŠs theorem. Fixed Point Theory Appl. vol. 2013, Article ID 129 (2013).
• Z. D. Mitrovic, On an open problem in rectangular b-metric spaces, Journal of Analysis, Vol.25, 135-137, (2017).
• B. Samet, C. Vetro, P. Vetro, Fixed point theorems for - -contractive type mappings, Nonlinear Analysis, vol.75, 2154- 2165, (2012).