New Fixed Point Theorems with Applications to Non-Linear Neutral Differential Equations

• Main Authors: Laila A. Alnaser, Jamshaid Ahmad, Durdana Lateef, Hoda A. Fouad
• Format: Article
• Language: English
• Published: MDPI AG 2019-04-01
• Series: Symmetry
• Subjects: nonlinear neutral differential equation; <named-content content-type="equation"><inline-formula> <mml:math id="mm2222" display="block"> <mml:semantics> <mml:mi mathvariant="script">F</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-metric space; (<named-content content-type="equation"><inline-formula> <mml:math id="mm1111" display="block"> <mml:semantics> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>φ</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>) rational contraction; fixed point
• Online Access: https://www.mdpi.com/2073-8994/11/5/602

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 (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#945;</mi> <mo>,</mo> <mi>&#966;</mi> </mrow> </semantics> </math> </inline-formula>) rational contraction, as well as cyclic contractions in the context of <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">F</mi> </semantics> </math> </inline-formula>-metric spaces. We also supply an example to support the new theorem.