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Search Results (3)

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Keywords = ( α , φ ) rational contraction

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11 pages, 273 KB  
Article
New Fixed Point Theorems with Applications to Non-Linear Neutral Differential Equations
by Laila A. Alnaser, Jamshaid Ahmad, Durdana Lateef and Hoda A. Fouad
Symmetry 2019, 11(5), 602; https://doi.org/10.3390/sym11050602 - 30 Apr 2019
Cited by 15 | Viewed by 2669
Abstract
The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized ( α , φ ) [...] Read more.
The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized ( α , φ ) rational contraction, as well as cyclic contractions in the context of F -metric spaces. We also supply an example to support the new theorem. Full article
12 pages, 261 KB  
Article
Common Fixed Point Results for Rational (α,β)φ- Contractions in Complete Quasi Metric Spaces
by Tariq Qawasmeh, Wasfi Shatanawi, Anwar Bataihah and Abdalla Tallafha
Mathematics 2019, 7(5), 392; https://doi.org/10.3390/math7050392 - 30 Apr 2019
Cited by 30 | Viewed by 2475
Abstract
The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational [...] Read more.
The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
15 pages, 318 KB  
Article
Common Fixed Point Theorem via Cyclic (α,β)–(ψ,φ)S-Contraction with Applications
by Mian Bahadur Zada, Muhammad Sarwar, Fahd Jarad and Thabet Abdeljawad
Symmetry 2019, 11(2), 198; https://doi.org/10.3390/sym11020198 - 11 Feb 2019
Cited by 4 | Viewed by 2674
Abstract
In this paper, we introduce the notion of cyclic ( α , β ) ( ψ , φ ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results [...] Read more.
In this paper, we introduce the notion of cyclic ( α , β ) ( ψ , φ ) s -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given. Full article
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