On fixed points of α-ψ-contractive multifunctions

Abstract

Abstract Recently Samet, Vetro and Vetro introduced the notion of α - ψ -contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce the notion of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mo>∗</mml:mo> </mml:msub> <mml:mtext>-</mml:mtext> <mml:mi>ψ</mml:mi> </mml:math> -contractive multifunctions and give a fixed point result for these multifunctions. We also obtain a fixed point result for self-maps in complete metric spaces satisfying a contractive condition.