On Fixed Point Theory for Generalized Contractions in Cone Rectangular Metric Spaces via Scalarizing

Parastoo Zangenehmehr, Ali Farajzadeh, Rahmatollah Lashkaripour, Ardashir Karamian

Abstract

In this paper, the eqivalency between versions of fixed point theorems in cone rectangular metric spaces and scalar versions of fixed point theorems in rectangular metric spaces is presented. Moreover, some fixed point theorems for generalized contractions in cone rectangular metric spaces are provided. The results of this paper can be considered as the improvment and extension of [W. S. Du, A  note on  cone metric fixed point theory and its equivalence, Nonlinear  Analysis, 72 (5) (2010),  2259-2261], [P. Ghosh, A charactrization of completeness of generalized metric spaces usind generalized Banach contraction principle Demonstratio mathematica, Vol. XLV, No 3, (2012) 717-724].