TY  - JOUR
T1  - On Fixed Point Results for Nonlinear Contractions in Fuzzy Cone Metric Space
AU  - Gerbeti, Dritan
AU  - Sila, Eriola
AU  - Duraj, Sidite
PY  - 2023
DA  - December
DO  - 10.55549/epstem.1404099
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 97
EP  - 102
VL  - 25
LA  - en
AB  - The study of Fixed Point Theory in various metric space has been on focus of scientific development for many authors. It has been advanced either by generalizing the contractive inequality or by extending the conditions of metric. Fuzzy metric space has been defined as space in which the distance between elements is not an exact number in difference with metric space. Fixed point Theory is an important framework point of view in fuzzy metric spaces. Many studies have been showed the existence and uniqueness of a fixed point for different type of contractions in these spaces. Nonlinear contractions and their generalizations have been under investigations in several metric spaces. The aim of this paper is the study of fixed points for generalized nonlinear contractions in fuzzy metric space. Our results guarantee the existence and uniqueness of a fixed point for these contractions and extend some known theorems in metric space to fuzzy metric space. As an application of main theorem an example is taken.
KW  - : Fixed point
KW  - Fuzzy cone metric space
KW  - Generalized nonlinear contraction
KW  - Auxiliary function
CR  - Alam, A., Sk, F., & Khan, H. Q. (2022) Discussion on generalized nonlinear contractions. U.P.B. Sci. Bull. Series A, 84(2), 23-34.
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CR  - Dutta, P. N., & Choudhury, B. S. (2008). A generalization of contraction principle in metric spaces, Fixed Point Theory Applications, 2008(1), 1-8.
CR  - George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399.
UR  - https://doi.org/10.55549/epstem.1404099
L1  - https://dergipark.org.tr/en/download/article-file/3596012
ER  -