Fixed Point Theorems via Orthogonal Convex Contraction in Orthogonal ♭-Metric Spaces and Applications

Abstract

In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of the solution for the spring-mass system via an integral equation with a numerical example.

Keywords

• ♭-metric space
• O-set
• O-sequence
• ♭_⊥-metric space
• fixed point
• orthogonal convex