Research Article New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces Muhammad Usman Ali , 1 Hassen Aydi , 2,3,4 and Monairah Alansari 5 1 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan 2 Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia 3 China Medical University Hospital, China Medical University, Taichung 40402, Taiwan 4 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa 5 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Correspondence should be addressed to Muhammad Usman Ali; muh_usman_ali@yahoo.com and Hassen Aydi; hassen.aydi@isima.rnu.tn Received 9 December 2020; Revised 31 December 2020; Accepted 4 January 2021; Published 18 January 2021 Academic Editor: Tuncer Acar Copyright © 2021 Muhammad Usman Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact. 1. Introduction There are numerous studies on interpolation inequalities in literature. In 1999, Chua [1] gave some weighted Sobolev interpolation inequalities on product spaces. Badr and Russ [2] proved some Littlewood-Paley inequalities and interpola- tion results for Sobolev spaces. Interpolation is considered as one of the central concepts in pure logic. Various interpola- tion properties find their applications in computer science and have many deep purely logical consequences (see [3, 4]). Gogatishvili and Koskela [5] presented variant interpola- tion properties of Besov spaces defined on metric spaces. Going in the same direction in the setting of metric spaces via contraction mappings, Karapinar [6] presented the con- cept of an interpolative Kannan contraction mapping and proved that this mapping admits a fixed point on complete metric spaces. Later on, this notation has been extended into several directions (see [7–18]). In [6], Karapinar presented the interpolative Kannan contraction as follows: a mapping K : ðW, d W Þ → ðW, d W Þ is an interpolative Kannan contraction if d W Kw a , Kw b  i ≤ δ d W w a , Kw a ð Þ ½  ι 1 d W w b , Kw b   h i 1−ι 1 ð1Þ for all w a , w b ∈ W with w a ≠ Kw a , where δ ∈ ½0, 1Þ and ι 1 ∈ ð0, 1Þ. This inequality was further refined by Karapinar et al. [7] by d W Kw a , Kw b  i ≤ δ d W w a , Kw a ð Þ ½  ι 1 d W w b , Kw b   h i 1−ι 1 ð2Þ Hindawi Journal of Function Spaces Volume 2021, Article ID 6641342, 8 pages https://doi.org/10.1155/2021/6641342