Abstract
In this paper, we prove some PPF dependent fixed point theorems in the Razumikhin class for some rational type contractive mappings involving -admissible mappings where the domain and range of the mappings are not the same. As applications of these results, we derive some PPF dependent fixed point theorems for these nonself-contractions whenever the range space is endowed with a graph. Our results extend and generalize some results in the literature. MSC:46N40, 47H10, 54H25, 46T99.
Highlights
The fixed point theory in Banach spaces plays an important role and is useful in mathematics
We show that T has a unique PPF dependent fixed point in Rc
For a fixed φ ∈ Rc, if the sequence {φn} of iterates of T is defined by Tφn– = φn(c) for all n ∈ N, {φn} converges to a PPF dependent fixed point of T in Rc
Summary
The fixed point theory in Banach spaces plays an important role and is useful in mathematics.
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