Research Article Nonunique Fixed Point Results via Kannan F -Contraction on Quasi-Partial b-Metric Space Pragati Gautam , 1 Santosh Kumar , 2 Swapnil Verma , 1 and Gauri Gupta 1 1 Department of Mathematics, Kamala Nehru College (University of Delhi), August Kranti Marg, New Delhi 110049, India 2 Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam, Tanzania Correspondence should be addressed to Santosh Kumar; drsengar2002@gmail.com Received 25 June 2021; Revised 17 July 2021; Accepted 1 October 2021; Published 2 November 2021 Academic Editor: Giovanni Di Fratta Copyright © 2021 Pragati Gautam 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. This paper is aimed at acquainting with a new Kannan F-expanding type mapping by the approach of Wardowski in the complete metric space. We establish some fixed point results for Kannan F-expanding type mapping and F-contractive type mappings which satisfy F-contraction conditions. Additionally, some new results are given which generalize several results present in the literature. Moreover, some applications and examples are provided to show the practicality of our results. 1. Introduction and Preliminaries In 1922, Banach [1] commenced one of the most essential and notable results called the Banach contraction principle, i.e., let P be a self-mapping on a nonempty set X and d be a complete metric, if there exists a constant k ∈ ½0, 1Þ such that d Pu, Pv ð Þ ≤ kd u, v ð Þ, ð1Þ for all u, v ∈ X. Then, it has a unique fixed point in X. Due to its significance, in 1968, Kannan [2] introduced a different intuition of the Banach contraction principle which removes the condition of continuity, i.e., for all u, v ∈ ½0, 1/2, there exists a constant ρ ∈ ½0, 1Þ such that d Pu, Pv ð Þ ≤ ρ du, Pu ð Þ + dv, Pv ð Þ ½ : ð2Þ On the other hand, the notion of metric space has been generalized in several directions, and the abovementioned contraction principle has been enhanced in the new settings by considering the concept of convergence of functions. In 1989, Bakhtin [3] introduced the notion of b-metric space which was revaluated by Czerwik [4] in 1993. Definition 1. A b-metric space on a nonempty set X is a function d : X × X ⟶ ½0,∞Þ such that for all u, v, w ∈ X and for some real number s ≥ 1, it satisfies the following: (M1) If dðu, vÞ =0, then u = v (M2) dðu, vÞ = dðv, uÞ (M3) dðu, wÞ ≤ s½dðu, vÞ + dðv, wÞ Then, the pair ðX, d, sÞ is called the b-metric space. Moti- vated by this, many researchers [5–8] generalized the con- cept of metric spaces and established on the existence of fixed points in the setting of b-metric space keeping in mind that, unlike standard metric, b-metric is not necessarily continuous due to the modified triangle inequality. In gen- eral, a b-metric does not induce a topology on X. Partial metric space is one of the attempts to generalize the notion of the metric space. In 1994, Matthews [9] intro- duced the notion of a partial metric space in which dðu, uÞ are no longer necessarily zero. Definition 2. A partial metric on a nonempty set X is a func- tion p : X × X ⟶ ½0,∞Þ such that for all u, v, w ∈ X, it satisfies the following: (PM1) If pðu, uÞ = pðu, vÞ = pðv, vÞ, then u = v (PM2) pðu, uÞ ≤ pðu, vÞ Hindawi Journal of Function Spaces Volume 2021, Article ID 2163108, 10 pages https://doi.org/10.1155/2021/2163108