Abstract
In this paper, we introduce some common fixed point theorems for interpolative contraction operators using Perov operator which satisfy Suzuki type mappings. Further, some results are given. These results generalize several new results present in the literature.
Highlights
Banach [1] introduced the Banach contraction principle that generalized in various wide directions by many researchers
One of the generalizations was supposed by Kannan [2] in 1968 and later with other researchers such as C′iric′ Reich Rus
Besides the hypothesis (i) and (ii) of Theorem 11, if we assume that the condition: (i) If fxrg is a sequence in P such that xr ⟶ x ∈ P as r ⟶ ∞ and, there exists a subsequence fxrk g of fxr g such that Λðxrk, xÞ ≥ I and Λðx, xrk Þ ≥ I, for all k holds, the mappings F and G have a common fixed point
Summary
Banach [1] introduced the Banach contraction principle that generalized in various wide directions by many researchers. Let ðP , dÞ be a complete vector-valued metric space and the operator F : P ⟶ P with the property that there exists a matrix A ∈ MmmðR+0 Þ convergent towards zero such that dðFðxÞ, FðzÞÞ ≤ Adðx, zÞ, for all x, z ∈ P : ð5Þ
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