(ρ, η, µ)-interpolative kannan contractions i

Yaé Ulrich Gaba; Hassen Aydi; Nabil Mlaiki

doi:10.3390/axioms10030212

(ρ, η, µ)-interpolative kannan contractions i

Yaé Ulrich Gaba^*, Hassen Aydi^*, Nabil Mlaiki

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

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.

Original language	English
Article number	212
Journal	Axioms
Volume	10
Issue number	3
DOIs	https://doi.org/10.3390/axioms10030212
Publication status	Published - Sept 2021
Externally published	Yes

Keywords

(ρ, η, µ)-interpolative Kannan contraction
Fixed point
Metric space

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10.3390/axioms10030212

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abstract = "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-{\'C}iri{\'c} type contraction.",

keywords = "(ρ, η, µ)-interpolative Kannan contraction, Fixed point, Metric space",

author = "Gaba, {Ya{\'e} Ulrich} and Hassen Aydi and Nabil Mlaiki",

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AU - Aydi, Hassen

AU - Mlaiki, Nabil

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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

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VL - 10

JO - Axioms

JF - Axioms

IS - 3

M1 - 212

ER -

(ρ, η, µ)-interpolative kannan contractions i

Abstract

Keywords

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