A note on fixed point theorems for weakly T-Kannan and weakly T-Chatterjea contractions in b-metric spaces

Abstract

In this paper, we consider fixed point results in the setup of $b$-metric spaces for weakly T-Kannan and weakly T-Chatterjea contractive mappings. Thus, we improve and complement recent results established by Z. Mustafa et al.\ [J.\ Inequal.\ Appl.\ 2014, 2014:46] and A. Razani, V. Parvaneh [Russ.\ Math.\ (Izv.\ VUZ), 57 (3), 38--45 (2013)], with much shorter proofs. Moreover, we show that the results of A.H. Ansari et al.\ [J. Inequal.\ Appl.\ 2014, 2014:429] are not generalizations of the known ones. An example is given illustrating our results.