Revising the Hardy–Rogers–Suzuki-type Z-contractions

Abstract

Abstract The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and Z $\mathcal{Z}$ -contraction. We investigate the existence of a fixed point of this type of mappings and prove some corollaries. The new results of the paper generalize a number of existing results which were published in the last two decades.

Keywords

• Fixed point
• Admissible contractions
• Interpolative
• Suzuki-type contractions
• w-regular