$C^{*}$-Valued contractive type mappings

Abstract

Abstract In this paper we generalize the notion of $C^{*}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -valued contraction mappings, recently introduced by Ma et al. , by weakening the contractive condition introduced by them. Using the new notion of $C^{*}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -valued contractive type mappings, we establish a fixed point theorem for such mappings. Our result generalizes the result by Ma et al. and those contained therein except for the uniqueness.