Common Fixed Point Theorems Involving Cubic Terms of d(x, y) in b-Metric Spaces

Objective/Aim: To establish the existence and uniqueness of fixed points for self maps in b-metric spaces. Methods: We have used generalized 𝜑-weak contractive condition involving cubic terms of d(x, y) and weak compatibility of two maps in the setting of b-metric spaces. Findings: Some fixed point theorems for a self map and common fixed point theorems for two maps have been proved and some suitable examples are also given to justify the proven results. Novelty: In b-metric spaces, the existence of fixed points for mappings satisfying generalized 𝜑-weak contractive conditions involving cubic terms of d(x, y) has not been proved yet by others. Furthermore, our results extend and generalize the results of Dutta and Choudhury, Murthy and Prasad, Hao and Guan, Jain and Kaur, Petru, sel, A. and Petru, sel, J., Peng et. al. etc. Mathematics Subject Classification: 54H25, 47H10. Keywords: Fixed Point, b-Metric Space, φ –Weak Contraction, Generalized φ –Weak Contraction, Weakly Compatible Mapping