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

Abstract

The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and $\mathcal{Z}$ 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.

A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions

“…From (24), we obtain Proof. Corollary can be obtained from Theorem 1 by taking α(s, u) = 1.□ Now we will propose some new results belonging to the class of Suzuki (α, F)contractions.…”

“…In the meantime, other recently defined concepts such as α-admissible mapping in [11] promoted in [12][13][14][15][16], Suzuki contraction widely used in [17][18][19][20][21], and formulations in partial metric spaces, metric-like spaces, b-metric spaces, and b-metric -like spaces underline their significance and offer a broader understanding in various contexts of the fixed point theory. For an extended introduction, we could mention many new theorems and corresponding classical results with applications in the above spaces, resulting in notions of interpolative and hybrid contractions; see [22][23][24].…”