On the Extended Version of Krasnoselśkiĭ’s Theorem for Kannan-Type Equicontractive Mappings

The purpose of the paper is to establish a sufficient condition for existence solution equation T(u,C(u))=u using Kannan-type equicontractive mappings, T:A×C(A)¯→Y, where C compact mapping, A bounded, closed and convex subset Banach space Y. To achieve this objective, authors have presented Sadovskii’s theorem, which utilizes measure noncompactness. relevance obtained results has been illustrated through consideration various initial value problems.