Fixed point theory in the setting of ( α , β , ψ , ϕ ) $(\alpha,\beta,\psi,\phi)$ -interpolative contractions

Abstract

Abstract In this manuscript we introduce the notion of ( α , β , ψ , ϕ ) $(\alpha,\beta,\psi,\phi)$ -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.

Keywords

• Interpolative contraction
• Kannan contraction
• Proinov contraction
• Ample spectrum contraction
• Fixed point