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SETSCI - Volume 3 (2018)
ISAS2018-Winter - 2nd International Symposium on Innovative Approaches in Scientific Studies, Samsun, Turkey, Nov 30, 2018

Nurcan Bilgili Güngör1*
1Amasya University, Amasya, Turkey
* Corresponding author: bilgilinurcan@gmail.com
Published Date: 2019-01-14   |   Page (s): 305-309
   |    40     8

ABSTRACT In 2012 Karapınar and Samet introduced the notion of α- contractive mappings and proved some well-known fixed point theorems. On the other hand in 2006 Mustafa and Sims gave the definition of G-metric space which is the generalization of metric space. In 2013 Algamdi and Karapınar combined these two notions as G-β - contractive mappings. They presented and proved related fixed point theorems. In this paper β-admissible mappings in G-metric spaces are restricted and some fixed point theorems are given. Our main results will give a new perspective to previous works in G-metrics. Indeed, as a result of a special selection of the given mappings, we obtained the main results of Algamdi and Karapınar as a conclusion  
REFERENCES [1] Alghamdi, M. and Karapınar, E., G-β- Contractive-Type Mappings in G-Metric Spaces, Fixed Point
Theory and Applications 2013, 2013:123.
[2] Alghamdi, M. and Karapınar, E., G-β- Contractive-Type Mappings and Related Fixed Point Theorems,
Journal of Inequalities and Applications 2013, 2013:151.
[3] Karapınar, E. and Samet, B., Generalized α − Contractive Type Mappings and Related Fixed Point
Theorems with Applications, Abstract and Applied Analysis 2012, Vol.2012, Hindawi.
[4] Mustafa, Z. and Sims, B., A new approach to generalized metric spaces, Journal of Nonlinear and Convex
Analysis 2006, 7(2),289-297.
[5] Salimi, P., Latif, A. and Hussain, N., Modified --contractive mappings with applications. Fixed Point
Theory and Applications, 2013, 2013(1), 151.

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