A Survey on Interpolative and Hybrid Contractions

Fixed point, its geometry, and application via ω‐interpolative contraction of Suzuki type mapping

“…Here, we utilize Suzuki type contraction, 17 $$$ \omega $$$‐orbital admissible mapping, 14 which is a generalization of $$$ \alpha $$$‐admissible mapping 15 . The obtained novel conclusions are validated by providing illustrative examples that generalize, extend, and improve numerous existing conclusions, which were obtained since the work of Karapinar 24 in this direction (see previous studies 8,11,26–32 and so on).…”

“…In 1930, Caccioppoli 1 enhanced and improved the conclusions of Banach 2 from normed space to metric space. Following him, numerous authors investigated many abstract spaces to generalize the conclusions of Banach 2 and Caccioppoli, 3 for instance, previous works [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and references therein. However, all such efforts were not beneficial, which was the main reason for the new explorations.…”

Fixed-Point Theorems for ω − ψ -Interpolative Hardy-Rogers-Suzuki-Type Contraction in a Compact Quasipartial b -Metric Space

“…Again in 2021, Khan et al [5] proved some fixed-point results on the interpolative ðϕ, ψÞ-type Z-contraction. For more results on interpolativetype contractions, one can see [6][7][8] and the references therein.…”

“…Then, there exists a unique fixed-point w ∈ M. A mapping f satisfying (7) is called as the Suzuki contraction.…”