Abstract. The main purpose of this paper is to establish some new results about the existence and uniqueness for coincidence problems for two single-valued mappings. Moreover, we present some applications of our results to the existence and uniqueness of solutions of some boundary value problems.
Let D(A) be the domain of an m-accretive operator A on a Banach space E. We provide sufficient conditions for the closure of D(A) to be convex and for D(A) to coincide with E itself. Several related results and pertinent examples are also included.Proof. Let x, y ∈ D(A), x = y, and t ∈ (0, 1) be given. Consider z := tx + (1 − t)y. We first prove that lim λ→0 + J λ (z) = z, and then it follows that z ∈ D(A), as required.To this end, fix u ∈ A(x), v ∈ A(y) and set u λ = x + λu, v λ = y + λv. It is clear thatand, consequently,Analogously, one can also check that J λ (z) − y z − y + λ v . Since E is reflexive, there exists a sequence (λ n ) such that λ n → 0 + and J λn z w ∈ X. By the weak lower semicontinuity of the norm, we have
We show that everyU-space and every Banach spaceXsatisfyingδX(1)>0areP(3)-convex, and we study the nonuniform version ofP-convexity, which we callp-convexity.
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