Some Remarks on Perov Type Mappings in Cone Metric Spaces

The contractivity of cone-preserving multilinear mappings

“…A Lipschitz matrix for f : M → M gives an estimate on the variation of f on each subspace (M i , µ i ). However, the next theorem shows that the spectral radius of such matrix provides an estimate on the variation of f on the whole space M. Since the seminal work of Perov [30], several authors have developed new fixed point results for vector valued and cone metric spaces (see for example [13,31,37] and the review [1]) and our next result contributes to this active line of research. In particular, note that such result extends the Banach fixed point theorem for cone-metrics (see e.g.…”

“…Since the seminal work of Perov [30], several authors have developed new fixed point results for vector valued and cone metric spaces (see for example [13,31,37] and the review [1]) and our next result contributes to this active line of research.…”

Common Fixed Point Theorem for Compatible Mappings of Type (P) in Multiplicative Cone Metric Space

“…They analysed convergence and substituted real numbers by ordered Banach space. After that, various authors proved and extend many fixed point and CFP (common fixed point) results to this space with normal and non-normal cone conditions (see, e.g., [3,6,8,9,11,12,13,14,16,17,18,19]).…”

Invariant approximations in Banach spaces

“…Later on an interesting and rich fixed point theory for such mappings developed; see [3] and the references therein. Inspired from the Nadler fixed point theorems [2], the fixed point theory of multivalued contractions was further developed in different directions by many authors, see, Beg and Azam [4], Feng and Liu [5], Kaneko [6], Klim and Wardowski [7], Lami Dozo [8], Lim [9], Mizoguchi and Takahashi [10], Pathak and Shahzad [11], Radenovic and Vetro [12], Reich [13,14], Suzuki [15].…”