‎inspired by the work of suzuki in‎ ‎[t. suzuki‎, ‎a generalized banach contraction principle that characterizes metric completeness‎, proc‎. ‎amer‎. ‎math‎. ‎soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of geraghty in [m.a‎. ‎geraghty‎, ‎on contractive mappings‎, ‎proc‎. ‎amer‎. ‎math‎. ‎soc., ‎40 (1973)‎, ‎604--608]‎an...

Abstract The purpose of this paper is to present the notion MR-Kannan type contractions using generalized averaged operator. Several examples are provided illustrate concept presented herein. We provide a characterisation normed spaces with fixed point. investigate Ulam–Hyers stability and well-posedness result for mappings here.

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.

in this paper, we prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. to prove the theorem, we use a non compatible condition, that is, weak commutativity of type (kb). we show that completeness of the whole space is not necessary for the existence and uni...