TY - JOUR
T1 - (ρ, η, µ)-interpolative kannan contractions i
AU - Gaba, Yaé Ulrich
AU - Aydi, Hassen
AU - Mlaiki, Nabil
N1 - Funding Information:
Acknowledgments: The first author would like to acknowledge that his contribution to this work was carried out with the aid of a grant from the Carnegie Corporation provided through the African Institute for Mathematical Sciences. The last author would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/9
Y1 - 2021/9
N2 - We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,µ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,µ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.
AB - We point out a vital error in the paper of Gaba et al. (2019), showing that a (ρ,η,µ) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (ρ,η,µ)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-Ćirić type contraction.
KW - (ρ, η, µ)-interpolative Kannan contraction
KW - Fixed point
KW - Metric space
UR - http://www.scopus.com/inward/record.url?scp=85114884318&partnerID=8YFLogxK
U2 - 10.3390/axioms10030212
DO - 10.3390/axioms10030212
M3 - Article
AN - SCOPUS:85114884318
SN - 2075-1680
VL - 10
JO - Axioms
JF - Axioms
IS - 3
M1 - 212
ER -