Fixed Point Theorems Over Extended ϕ,ψ-Metric Spaces and Applications in Differential Equations - Mohammed M. A. Taleb; Saeed A. A. Al-Salehi; V. C. Borkar (Journal of Function Spaces)
The main aim of this research endeavor is to introduce a novel type of generalized metric space, termed an extended ϕ,ψ-metric space, to establish new fixed point results and employ them to prove the existence and uniqueness of solutions to first-order differential equations. To achieve this goal, we introduce the concepts of α,θ-admissible Banach contraction, α,θ-admissible crooked Banach contraction, and α,θ-admissible φ,β-contraction in an extended ϕ,ψ-metric space. We augment our theoretical results by providing compelling and nontrivial illustrative examples.