In this paper, we provide a short, comprehensive, and brief proof for Caristi-Kirk fixed point result single set-valued mappings in cone metric spaces. addition, partially addressed an open problem which spaces reduces to classical provided justification partial positive answer using theorem on uniform space. The proofs given Caristi-Kirk’s vary use different techniques.

This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over locally convex Hausdorff topological vector space. ensures that most studies on existence uniqueness of fixed-point theorems space spaces are equivalent. We prove vector-valued version scalar-valued those spaces. Moreover, we present if real Banach is considered inst...