Tripled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

Abstract

Tripled fixed points are extensions of the idea of coupled fixed points introduced in a recent paper by Berinde and Borcut, 2011. Here using a separate methodology we extend this result to a triple coincidence point theorem in partially ordered metric spaces. We have defined several concepts pertaining to our results. The main results have several corollaries and an illustrative example. The example shows that the extension proved here is actual and also the main theorem properly contains all its corollaries.

Coupled and Tripled Coincidence Point Results with Application to Fredholm Integral Equations

“…In the following theorem, we give a sufficient condition for the uniqueness of the common coupled fixed point (see also [25,28,30]).…”

“…so lim → ∞ inf ( , −1 , −1 ) = 0, a contradiction to (28). It follows that { } is a -Cauchy sequence in .…”

“…On the other hand, Berinde and Borcut [25] introduced the concept of tripled fixed point and obtained some tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. For a survey of tripled fixed point theorems and related topics we refer the reader to [25][26][27][28]30].…”

A tripled fixed point technique for solving a tripled-system of integral equations and Markov process in CCbMS

“…Pivotal results related to a TFP (established in 2011 by Berinde and Borcut [22]) were presented in partially ordered metric spaces. For more topics of this notion, we refer to [23][24][25][26][27][28][29][30].…”

A technique of tripled coincidence points for solving a system of nonlinear integral equations in POCML spaces

“…Pivotal results related to a triple fixed point (established in 2011 by Berinde and Borcut [28]) were presented in partially ordered metric spaces. For more topics of this notion, we cite papers [29][30][31][32][33][34][35]. Definition 1.1 ([28]) It is said that a trio (℘, , ð) ∈ χ 3 is a tripled fixed point of a selfmapping : χ 3 → χ if ℘ = (℘, , ð), = ( , ℘, ), and ð = (ð, , ℘).…”