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Article

PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications

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Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
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Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
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Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
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Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
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China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(11), 1375; https://doi.org/10.3390/sym11111375
Received: 27 September 2019 / Revised: 20 October 2019 / Accepted: 21 October 2019 / Published: 6 November 2019
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of f ( x ) = x . One of such examples is that of the famous Borsuk–Ulam theorem, in which using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this paper, we initiate ϕ F -contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering. View Full-Text
Keywords: PPF-dependent fixed point; ϕ-F-contractions; the Razumikhin class; Banach space PPF-dependent fixed point; ϕ-F-contractions; the Razumikhin class; Banach space
MDPI and ACS Style

Jaradat, M.M.M.; Mohammadi, B.; Parvaneh, V.; Aydi, H.; Mustafa, Z. PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications. Symmetry 2019, 11, 1375. https://doi.org/10.3390/sym11111375

AMA Style

Jaradat MMM, Mohammadi B, Parvaneh V, Aydi H, Mustafa Z. PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications. Symmetry. 2019; 11(11):1375. https://doi.org/10.3390/sym11111375

Chicago/Turabian Style

Jaradat, Mohammed M.M., Babak Mohammadi, Vahid Parvaneh, Hassen Aydi, and Zead Mustafa. 2019. "PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications" Symmetry 11, no. 11: 1375. https://doi.org/10.3390/sym11111375

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