Let R be a commutative ring with unity. The notion of λ-rings, φ-λ-rings, and φ-∆-rings is introduced which generalize the concept of λ-domains and ∆-domains. A ring R is said to be a λ-ring if the set of all overrings of R is linearly ordered under inclusion. A ring R ∈ H is said to be a φ-λ-ring if φ(R) is a λ-ring, and a φ-∆-ring if φ(R) is a ∆-ring, where H is the set of all rings such that Nil(R) is a divided prime ideal of R and φ : T(R) → RNil(R) is a ring homomorphism defined as φ(x) = x for all x ∈ T(R). The equivalence of φ-λ-rings, φ-∆-rings with the latest trending rings in the literature, namely, φ-chained rings and φ-Prüfer rings is established under some conditions. Using the idealization theory of Nagata, examples are also given to strengthen the concept