Multidimensional Fixed-Point Theorems in Partially Ordered Complete Partial Metric Spaces under ()-Contractivity Conditions

Abstract

We study the existence and uniqueness of coincidence point for nonlinear mappings of any number of arguments under a weak ()-contractivity condition in partial metric spaces. The results we obtain generalize, extend, and unify several classical and very recent related results in the literature in metric spaces (see Aydi et al. (2011), Berinde and Borcut (2011), Gnana Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapınar and Luong (2012), Lakshmikantham and Ćirić (2009), Luong and Thuan (2011), and Roldán et al. (2012)) and in partial metric spaces (see Shatanawi et al. (2012)).

Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

“…The idea under consideration was initiated by Turinici [17], which was later generalized by several authors, e.g., Ran and Reurings [18], Nieto and Rodríguez-López [19], and some others, e.g., the authors of [34][35][36][37]. In this section, from now on, denotes a partial order on a non-empty set M, (M, ) denotes a partially ordered set, and (M, ρ, ) stands for a partial metric space with partial order , which we call ordered partial metric space.…”

Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

“…• monotone if it is either non-decreasing or non-increasing. If (X, d, ) is an ordered distance space and g : X → X is a mapping, then (X, d, ) is said to have the sequential g-monotone property [37,68] if it verifies: i) if {x n } n∈N is a non-decreasing sequence and lim n→∞ d(x, x n ) = 0, then g(x n ) g(x) for all n ∈ N; ii) if {x n } n∈N is a non-increasing sequence and lim n→∞ d(x, x n ) = 0, then g(x n ) g(x) for all n ∈ N. An ordered distance space (X, d, ) is called monotonically complete if any monotone Cauchy sequence in X converges to some point in X.…”

Multidimensional coincidence point results for generalized $(\psi ,\theta ,\varphi)$-contraction on ordered metric spaces

“…However, they used permutations of variables and distinguished between the first and the last variables. For more details one can refer ( [11], [18], [19], [20], [21], [22], [26], [30], [31], [32], [34], [38]). In this research paper, we obtain some coincidence point theorem for g-non-decreasing mappings under generalized (ψ, θ , φ)-contraction on a partially ordered metric space.…”