Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces
By Ljubomir Ciric, Nenad Cakic, Miloje Rajovic, J. Ume. 2008
289 citations recorded by the source corpus.
A concept of -monotone mapping is introduced, and some fixed and common fixed point theorems for -non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. (2008).
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a4d1b8aed39704817ec7998feff961334178163c
How researchers see this paper
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In Geometry and Topology
- Bessem Samet
- Ljubomir Ciric
- Hassen Aydi
- Ravi P. Agarwal
- Calogero Vetro
- Nawab Hussain
- Mujahid Abbas
- Dorel Mihet
Citations in the corpus
- Nonlinear contractions involving simulation functions in a metric space with a partial order (2015, result): “Further, several results appeared in this direction, we mention [1, 2, 3, 4, 5, 7, 8, 9, 10, 13] and the references therein.”
- FIXED POINT THEOREMS FOR GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED PARTIAL METRIC SPACES (2011, background): “On the other hand, fixed point problems of contractive mappings in metric spaces endowed with a partially order have been studied by many authors (see [1, 3, 5, 9, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21]).”
- Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces (2011, methodology): “The main idea in [2-11] involve combining the ideas of iterative technique in the contraction mapping principle with those in the monotone technique.”
- 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).”
- 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]).”