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