On Pata–Suzuki-Type Contractions

Abstract

In this manuscript, we introduce two notions, Pata−Suzuki Z -contraction and Pata Z -contraction for the pair of self-mapping g , f in the context of metric spaces. For such types of contractions, both the existence and uniqueness of a common fixed point are examined. We provide examples to illustrate the validity of the given results. Further, we consider ordinary differential equations to apply our obtained results.

Keywords

• simulation function
• pata–suzuki <i>ƶ</i>-contraction
• <i>ƶ</i>-contraction
• <i>c</i>-condition