Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce a new class of mappings called the generalized orthogonal $F$-Suzuki contraction for a family of multivalued mappings in the setup of orthogonal $b$-metric spaces. We established the existence of some common fixed point results without using any commutativity condition for this new class of mappings in orthogonal $b$-metric spaces. Moreover, we illustrate and support these common fixed point results with example. The results obtained in this work generalize and extend some recent and classical related results in the existing literature.

Keywords: Orthogonal $b$-metric space, $\perp$-preserving, generalized $F$-Suzuki contraction, common fixed point

MSC numbers: Primary 47H10, 47H04, 47H07

Supported by: The research of the first author is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. The research of the first author is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support.