Abstract In this paper, we first introduce several new contractions by some auxiliary functions. Then establish φ -fixed point results for $(\gamma ,\psi ,\varphi ,\phi )$ ( γ , ψ φ ϕ ) contractions, rational...

We study interior Lp-regularity theory, also known as Calderon-Zygmund of the equation〈Lsu,φ〉:=∫Rn∫RnK(x,y)(u(x)−u(y))(φ(x)−φ(y))|x−y|n+2sdxdy=〈f,φ〉,∀φ∈Cc∞(Rn). prove that for s∈(0,1), t∈[s,2s], p∈[2,∞), K an elliptic, symmetric, and K(⋅,y) is uniformly Hölder continuous, solution u belongs to Hloc2s−t,p(Ω) long 2s−t<1 f∈(H00t,p′(Ω))⁎. The increase in differentiability integrability independent...

We investigate modal logical aspects of provability predicates PrT(x) satisfying the following condition: M: If T⊢φ→ψ, then T⊢PrT(⌜φ⌝)→PrT(⌜ψ⌝). prove arithmetical completeness theorems for monotonic logics MN, MN4, MNP, MNP4, and MND with respect to condition M. That is, we that each logic L them, there exists a Σ1 predicate M such is exactly L. In particular, formulas P: ¬□⊥ D: ¬(□A∧□¬A) are ...

Very recently, by considering a self-mapping T on complete metric space satisfying general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in literature. Accordingly, inspired Proinov-type contraction conditions, Roldán López de Hierro et al. introduced novel family contractions fuzzy spaces (i...

Well-posedness of constrained minimization problems via saddle-points BIAGIO RICCERI Dedicated to Professor Jean Saint Raymond on his sixtieth birthday, with my greatest admiration and esteem Here and in the sequel, X is a Hausdorff topological space, J, Φ are two real-valued functions defined in X, and a, b are two numbers in [−∞, +∞], with a < b.

The unification problem in a propositional logic is to determine, given formula φ, whether there exists substitution σ such that σ(φ) logic. In case, unifier of φ. When unifiable has minimal complete sets unifiers, it either infinitary, finitary, or unitary, depending on the cardinality its unifiers. Otherwise, nullary. this paper, we prove modal $\mathbf {K}+\square \square \bot $ , formulas a...