New fixed point theorems for $${\alpha}$$ α - $${H\Theta}$$ H Θ -contractions in ordered metric spaces
| Autor: | Vahid Parvaneh, Nawab Hussain, Farhan Golkarmanesh, Peyman Salimi |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Mathematical analysis Fixed-point theorem Periodic point Fixed point 01 natural sciences General family 010101 applied mathematics Metric space Modeling and Simulation Geometry and Topology 0101 mathematics Contraction principle Mathematics |
| Zdroj: | Journal of Fixed Point Theory and Applications. 18:905-925 |
| ISSN: | 1661-7746 1661-7738 |
| DOI: | 10.1007/s11784-016-0330-z |
| Popis: | Recently, Jleli and Samet [J. Inequal. Appl. (2014), 2014:38] introduced and studied a new contraction to prove a generalization of the Banach contraction principle. In this paper, we introduce the concept of \({\alpha}\)-\({H\Theta}\)-contraction with respect to a general family of functions H and we establish Jleli–Samet-type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki-type fixed point results for \({H\Theta}\)-contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized \({\Theta}\)-contractions. Moreover, we present an illustrative example to highlight the obtained improvements. |
| Databáze: | OpenAIRE |
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