Some Fixed Point Results of (α,β,φ,δ) Contractions in Extended Cone b-Metric Spaces

Abstract

This paper investigates the existence and uniqueness of fixed points for a class of generalized contractive mappings defined on extended cone metric spaces. Subsequently, we define and explore (α, β, φ, δ)-contractions, a generalization of traditional contractions that allows for a more nuanced understanding of the contraction behavior in extended cone metric spaces. The extended metric space was defined for the first time in 2017, by Kamran et al. (2017). They replaced the constant in the triangle inequality of the metric with a two-variable function and explored various fixed point theorems. In 2022, Das and Bag[4] introduced extended cone metric spaces by incorporating a three-variable map into the third condition of the cone metric. Afterwards, Selko and Sila introduced the concept of extended quasi cone b-metric spaces and demonstrated the Banach contraction within this framework. In 2018, Alqahtani. (2018) and colleagues established several fixed point results for a pair of orbital cyclic functions in an extended metric space. In this paper we prove some fixed point theorems for -orbital-cyclic functions in extended cone metric spaces by using the continuous map φ and a nonnegative constant δ.

Keywords

• (αβ)-orbital-cyclic functions
• Fixed point
• Extended cone metric space
• Cone metric space

References

1. Alqahtani, B., Fulga, A. & Karapınar, E. (2018). Common fixed point results on an extended b-metric space. Journal of Inequalities and Applications, 158.
2. Czerwik, S. (1993). Contraction mappings in b-metric spaces." Acta Mathematica et Informatica Universitatis Ostraviensis, 1(1), 5-11. Retrieved from http://eudml.org/doc/23748.
3. Das, A., & Bag, T. (2022). Some fixed point theorems in extended cone -metric spaces. Communications in Mathematics and Applications, 13(2), 647–659.