Abstract
The goal of this study is to propose a new interpolative contraction mapping by using an interpolative approach in the setting of complete metric spaces. We present some fixed point theorems for interpolative contraction operators using w -admissible maps which satisfy Suzuki type mappings. In addition, some results are given. These results generalize several new results present in the literature. Moreover, examples are provided to show the suitability of our given results.
Highlights
In 1922, Banach [1] proved his famous remarkable fixedpoint theorem; the result is known as the Banach contraction principle, which states that “Let ðK, dÞ be a complete metric space and S : K ⟶ K be a contraction, S has a unique fixed point.”
We introduce new concepts on completeness of w-ψ-interpolative Kannan contraction of Suzuki type and w-ψ-interpolative Ćirić-Reich-Rus contraction of Suzuki type mappings in metric space
We obtain some fixed point results and give examples to show that the new results are applicable
Summary
In 1922, Banach [1] proved his famous remarkable fixedpoint theorem; the result is known as the Banach contraction principle, which states that “Let ðK, dÞ be a complete metric space and S : K ⟶ K be a contraction, S has a unique fixed point.” The Banach contraction principle is one of the essential and most valuable theorems of analysis and is accepted as the main results of metric fixed-point theory. In 1922, Banach [1] proved his famous remarkable fixedpoint theorem; the result is known as the Banach contraction principle, which states that “Let ðK, dÞ be a complete metric space and S : K ⟶ K be a contraction, S has a unique fixed point.”. The Banach contraction principle is one of the essential and most valuable theorems of analysis and is accepted as the main results of metric fixed-point theory. Due to several applications of “fixed point theory,” researchers were motivated to further generalize it in different directions, by generalizing the contractive conditions underlying the space concept of completeness. The background literature on the famous Banach contraction principle has been extended in various comprehensive directions by many researchers.
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