Some Fixed Point Theorems on Ordered Metric Spaces and Application

By Ishak Altun, Hakan Simsek. 2010

292 citations recorded by the source corpus.

We present some fixed point results for nondecreasing and weakly increasing operators in a partially ordered metric space using implicit relations. Also we give an existence theorem for common solution of two integral equations.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5811a9dba726ab2cd7b1dbe85b7a754b1f4845e0

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In Geometry and Topology

Citations in the corpus

Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “There exist a vast literature concerning its various generalizations and extensions (see [1-45]).”
Some Coincidence Point Theorems for Nonlinear Contraction in Ordered Metric Spaces (2011, background): “Introduction and Preliminaries Generalization of the Banach principle [1] has been heavily investigated by many authors (see [2-14]).”
Coupled fixed points in partially ordered metric spaces and application (2011, unknown): “The existence of solutions for matrix equations or ordinary differential equations by applying fixed point theorems are presented in [8,2,9,3,4,1].”
FIXED POINT THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED PARTIAL METRIC SPACES (2011, background): “There exist some examples to illustrate this fact in [3]”
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations (2012, result): “The obtained result in [19] was further extended and refined by many authors (see, for example, [2, 3, 10, 12, 16, 17, 18] and the references cited therein).”