Coupled fixed points for Chatterjea type maps with the mixed monotone property in partially ordered metric spaces

Coupled Fixed Points Results for Hardy–rogers Type of Maps With the Mixed Monotone Property Obtained With the Help of a Variational Technique

“…Thus we generalize the results from [16,25] 2 Preliminaries Definition 1. ( [3,13]) Let (X, ⪯) be a partially ordered set and let F : X × X → X.…”

“…If we take α = γ = 0 in Theorem 3 we get the result from [25]. If we take α = β = 0 in Theorem 3 we get a result from [16].…”

“…In [25] Ekeland's variational principle is generalized on classes of subsets of partially ordered complete metric spaces (X, ⪯) with a function F : X × X → X, which have the mixed monotone property. Later one the idea from [25] is used in [16] to obtain an existence and uniqueness of coupled fixed points for maps with the mixed monotone property in partially ordered metric spaces that satisfy a kind of Chaterjea contraction.…”