Impact of Common Fixed Point Theorems Involving Cubic Terms of d (p, q) in b-Metric Space

Abstract Objective/Aim: To demonstrate the existence and uniqueness of fixed points for self-maps in b-metric spaces, we utilized a generalized 𝜙-weak contractive condition that incorporates cubic terms of d(x, y), along with the weak compatibility of two mappings within the context of b-metric spaces. Our findings include the proof of various fixed point theorems for a self-map, as well as common, point theorems for two mappings, accompanied by appropriate examples to substantiate the established results. The innovative aspect of our work lies in proving the existence of fixed points for mappings that meet generalized 𝜙-weak contractive conditions with cubic terms of d(x, y) in b-metric spaces, a result that has not been previously established by others. Furthermore, our results serve to extend,discribe and generalize the findings of Dutta and Choudhury, Murthy and Prasad, Hao and Guan, Jain and Kaur, Petru, sel, A. and Petru, sel, J., Peng et al., among others.Ues for other fixed point theorem and improve with work. Mathematics Subject Classification: 54H25,47H10.