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

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 ) rational contraction, as well as cyclic contractions in the context of F -metric spaces. We also supply an example to support the new theorem.

Some Generalized Fixed Point Results with Applications to Dynamic Programming

“…is F-convergent to ζ * . Afterwards, many researchers [2][3][4][5][6][7][8][9] worked in this space.…”

“…Recently, Jlei and Samet [1] initiated a generalized metric space named as F-metric space and showed a generalization of the Banach contraction principle. Meanwhile, researchers have picked keen interests in extending results in this generalized metric space; see for instance, [2][3][4][5]. In this paper, we define some generalized contractions and establish some results in the context of F-metric spaces.…”

Advancements in Best Proximity Points: A Study in F-Metric Spaces with Applications

“…Some coupled best proximity points on F -metric spaces endowed with an arbitrary binary relation are also established by Lateef [10]. For further details from this standpoint, we direct readers to [11][12][13][14][15][16][17][18][19][20]. In this manuscript, we introduce the notion of (α, Θ)-proximal contraction within the framework of F -metric space, establishing the existence and uniqueness of best proximity points for these contractions.…”