Some new results for a class of multivalued interpolative Kannan-type contractions
Date
2022
Authors
Konwar, Nabanita
Srivastava, Rekha
Debnath, Pradip
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Axioms
Abstract
In this paper, we introduce the notion of multivalued interpolative Kannan-type contractions.
We also introduce a more general version of this notion by relaxing the degrees of freedom of
the powers arising in the contractive condition. Gaba et al. (2021) recently pointed out a significant
error in the paper of Gaba and Karapinar (2019), showing that a particular type of generalized interpolative
Kannan-type contraction does not posses a fixed point in general in a complete metric space.
Thus, the study of generalized Kannan-type mappings remains an interesting and mathematically
challenging area of research. The main aim of this article is to address such existing results for
multivalued mappings. We also investigate common fixed points for this type of contractions. Our
results extend and unify some existing results in the literature.
Description
Keywords
fixed point, Kannan-type contraction, interpolative map, multivalued map, contraction map, common fixed point, differential equation, integral equation, metric space
Citation
Konwar, N., Srivastava, R., Debnath, P., & Srivastava, H. (2022). “Some new results for a class of multivalued interpolative Kannan-type contractions.” Axioms, 11(2), 76. https://doi.org/10.3390/axioms11020076