The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.

In this paper, for a unital -algebra A, we introduce a version of --contractive mappings in -algebra valued b-metric spaces, and we prove some Banach fixed point theorems and give some examples to illustrate our results.

In this paper, fixed point theorems using ψ contractive mapping in ${\mathrm{C}}^{\ast }$-algebra valued b-metric space are introduced. By stating multiple scenarios that illustrate the application domains, we demonstrate several applications from the obtained results. In particular, we begin with the definition of the positive function and then recall some properties of the function that lay the fundamental basis for the research. We then study some fixed point theorems in the ${\mathrm{C}}^{\ast }$-algebra valued b-metric space using a positive function.

In this present paper, we establish the existence and uniqueness of the common fixed point theorem for self-maps in C*-algebra valued b-metric spaces. Besides, we give example to illustrate our theorem. Findings obtained in this paper unify, generalize, and complement the comparable results from the current literature.