Abstract
The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function b(c,d): mhc,d,t+s+u+v+w≥mhc,e,tb(c,d)∗mhe,f,sb(c,d)∗mhf,g,ub(c,d)∗mhg,k,vb(c,d)∗mhk,d,wb(c,d) for all t,s,u,v,w>0 and c≠e,e≠f,f≠g,g≠k,k≠d. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained.
Highlights
Introduction and PreliminariesFollowing Banach’s significant approach to fixed point theory based on the fixed point concept, the majority of the authors offered several research studies on this topic.Zadeh [1] proposed a fuzzy set in 1965, which generalised the notion of the crisp set by combining all elements with membership values in the interval [0, 1]
This section begins with an introductory of fuzzy extended hexagonal b-metric spaces, as well as an example of the space defined
In the context of fuzzy extended hexagonal b-metric spaces, we demonstrate a fixed point theorem as given below: Theorem 2
Summary
Following Banach’s significant approach to fixed point theory based on the fixed point concept, the majority of the authors offered several research studies on this topic. Zadeh [1] proposed a fuzzy set in 1965, which generalised the notion of the crisp set by combining all elements with membership values in the interval [0, 1]. Following the implementation of Zadeh’s fuzzy topic, many researchers [2,3,4,5] expanded on the fuzzy metric area of study and developed certain results. Brought the theory of fuzzy metric spaces. Grabiec [7] established the fuzzy form of Banach contraction mapping principle. Bakhtin [8], Bourbaki [9], and Czerwik [10] all contributed to the development of the ideology of fixed points for b-metric spaces. Kamran et al [11]
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