Research Article

The role of concave functions in the study of interpolative contractions


Abstract

The interpolative contraction and its numerous generalizations motivated this study on its relation to previously known classes of contractive mappings. We will prove that by using of the concave property of the logarithmic function (or Jensen’s inequality), it is possible to relate some observed classes of interpolative contraction to their classical analogues. The theoretical results are substantiated with several examples.

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