A unique common coupled fixed point theorem for four maps under Ψ-Φ contractive condition in partial metric spaces

Abstract

In this paper, we obtain a unique coupled common fixed point theorem for four maps in partial metric spaces. RESUMEN En este artículo obtenemos un teorema del punto fijo clásico acopladoúnico para cuatro aplicaciones en espacios métricos parciales.

A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations

“…Therefore, condition (2) holds with τ = 7 and p = 5. By Corollary 1, system (20) has a unique solution (κ * , µ * ) ∈ C[0, 1] × C[0, 1].…”

“…Another direction, the coupled fixed point, was introduced and studied by Bhaskar and Lakhsmikantham [13]. They studied coupled fixed point results by using suitable contraction mappings and applied their results to show the existence of solutions for a periodic boundary value problem, so it has been a subject of interest by many researchers in this direction, (see, for example [14][15][16][17][18][19][20][21]).…”

Unique Common Fixed Point Theorems for Pairs of Hybrid Maps under a New Condition in Partial Metric Spaces

“…Suppose z 1 is another common fixed point of f, g, S and T . From (8), we have (12) ppz, z 1 q " ppf z, gz …”

“…He presented a modified version of the Banach contraction principle, more suitable in this context, see also [3,6]. In fact, the partial metric spaces constitute a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory, see [4,5,7,10,11,12,13,16,21,22]. In this direction, Aydi et al [9] introduced the concept of a partial Hausdorff metric and extended Nadler's fixed point theorem in the setting of partial metric spaces.…”

A Suzuki type unique common fixed point theorem for two pairs of hybrid maps under a new condition in partial metric spaces

“…In fact, the partial metric spaces offer a suitable framework to model several distinguished examples of the theory of computation and also to model metric spaces via domain theory (e.g. [4,5,7,8,18,19,20,21,22,23,24]). In this direction, Aydi et al [1] introduced the concept of a partial Hausdorff metric and extended Nadler's fixed point theorem to the setting of partial metric spaces.…”