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

Abstract

Abstract In this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:math> -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.

Topics & Concepts