Should instead read: Let (( X,sigma_{b} ) ) be a complete b-metric-like space with parameter (s ge 1), (f:X to X) be a self-mapping, and (alpha :X times X to mathopen[ 0,infty mathclose) ).
Let (X, d) be a complete metric space, T is self-mapping, (T: Xrightarrow X), and (alpha : Xtimes X rightarrow mathbb {R}).
In 2012, Samet et al. [15] introduced the concepts of (alpha -contractive alpha -contractiveible mandings alpha -admissiblealpha -admissiblet theoremappingsuch cland of mappings destablishedomplete metric spaces.
In this direction, Samet et al. [8] introduced the concept of α-admissible, α-contractive, and (alpha - psi -contractive mapsi -contractiveextended to the ((alpha,beta ) )-contractive mappings.
Let X be a nonempty set, (T :Xto X) and (alpha : Xtimes Xto[0,infty)) be two mappings. We say that T is an α-admissible mapping if (alpha x, y ge1) implies (alpha (Tx, Ty ge1), for all (x, y in X). Let ((X,d)) be a GMS and (alpha Xtimes Xto[0,infty)).
Let X be any nonempty set and (T : X rightarrow X) and (alpha : X times X rightarrow [0, infty )) be mappings.
Let ((chi,d_{mathrm {lc}})) be a dCMS-BA, (T : X rightarrow X) and (alpha : X times X rightarrow [0, infty )) be mappings.
Let ((chi,d_{mathrm {lc}})) be a dCMS-BA, (Tcolon chi rightarrow chi ) and (alpha : X times X rightarrow [0, infty )) be mappings.
The results have been established for (alpha psi) contractive mappings and for a generalized (beta -type one.
Let X be a nonempty set, (T : Xrightarrow N X)) and (alpha: X times X rightarrow[0,infty)) be two given mappings.
In [11] Samet et al. introduced the concept of α-admissible mappings and proved fixed point theorems for alpha-psi contractive-type mappings, which paved the way for proving new and existing results in fixed point theory.
