Abstract
In this paper, using an interpolative approach, we investigate two fixed point theorems in the framework of a b-metric space whose all closed and bounded subsets are compact. One of the theorems is for set-valued Hardy–Rogers-type and the other one is for set-valued Reich–Rus–Ćirić-type contractions. Examples are provided to validate the results.
Highlights
After Banach proved the celebrated contraction principle [1] in 1922, numerous researchers have tried to improve or generalize it
The generalizations were mainly done in two directions—either the contractive condition was replaced by some more general ones, or new metric spaces were defined by incorporating additional conditions
We prove a fixed point theorem for set-valued Reich–Rus–Ćirić-type contraction in b-metric spaces
Summary
After Banach proved the celebrated contraction principle [1] in 1922, numerous researchers have tried to improve or generalize it. The generalizations were mainly done in two directions—either the contractive condition was replaced by some more general ones, or new metric spaces were defined by incorporating additional conditions. In the former direction, many significant and improved results appeared, like Kannan’s [2], Chatterjea’s [3], Ćirić’s [4], Meir-Keeler’s [5], Boyd-Wong’s [6], etc. Some of them were not even true generalizations as they appeared to be equivalent to already existing ones. For some recent relevant work we refer to the works by the authors of [7,8,9]
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