Existence results for neutral functional differential inclusions in Banach algebras

Existence theorems for hyperbolic differential inclusions in Banach algebras

“…Thus our Theorem 2.1 is an improvement upon a multi-valued hybrid fixed point theorem proved in Dhage [5].…”

“…We apply the following slight improvement of a fixed point theorem of Dhage [5] in the sequel. Then either (i) the operator inclusion x ∈ Ax Bx has a solution, or (ii) the set E = {u ∈ X: μu ∈ Au Bu, μ > 1} is unbounded.…”

“…Theorem 2.1 above is proved in Dhage [5] under the additional hypothesis that (d) Ax Bx is a convex subset of X for each x ∈ X.…”

Existence of solutions for a class of boundary value problems of semilinear differential inclusions

“…Lemma 2.10 (See [26,27]). Let F : I × R n R n be a u-Carathéodory multivalued map with compact values and S 1 F (x) ̸ = ∅ for all x ∈ C (I, R n ), and let Γ : L 1 (I, R n ) → C (I, R n ) be a continuous linear operator.…”

Nonlocal boundary value problems for hybrid fractional differential equations and inclusions of Hadamard type

“…This paper investigates the existence of solutions for nonlocal boundary value problems of nonlinear hybrid fractional differential equations and inclusions of Hadamard type. We make use of fixed point theorems due to Dhage [7], [8] to obtain the existence results. We also discuss some examples for illustration of the main results.…”