a new class of nonlinear set-valued variationalinclusions involving $(a,eta)$-monotone mappings in a banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(a,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

‎In this paper‎, ‎using a generalized translation operator‎, ‎we obtain a generalization of Younis Theorem 5.2 in [3] for the Cherednik-Opdam transform for functions satisfying the $(delta,gamma,p)$-Cherednik-Opdam Lipschitz condition in the space‎ ‎$L^{p}_{alpha,beta}(mathbb{R})$.

Suppose that $f$ is a $K$-quasiconformal self-mapping of the unit disk $\mathbb{D}$, which satisfies following: $(1)$ biharmonic equation $\Delta(\Delta f)=g$ $(g\in \mathcal{C}(\overline{\mathbb{D}}))$, (2) boundary condition $\Delta f=\varphi$ ($\varphi\in\mathcal{C}(\mathbb{T})$ and $\mathbb{T}$ denotes circle), $(3)$ $f(0)=0$. The purpose this paper to prove Lipschitz continuos, and, furthe...

We study Daugavet points and $\Delta $-points in Lipschitz-free Banach spaces. prove that if $M$ is a compact metric space, then $\mu \in S_{\mathcal F(M)}$ point only there no denting of $B_{\mathcal at distance

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).  

We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar kernel and nonlinear parabolic equations (of ordinary type, with nonlinear conservative term and with Schrödinger kernel) with strongly singular initial data a...

We give a new characterization of the Baire class 1 functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions, which are particularly simple Lipschitz functions. Moreover we highlight the link between the two classical stratifications of the Borel functions by showing that the Baire class functions of some level are exactly ...

Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K aF is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the fi...

We show that, for a separable and complete metric space $M$, the Lipschitz-free $\mathcal F(M)$ embeds linearly almost-isometrically into $\ell_1$ if only $M$ is subset of an $\mathbb R$-tree with length measure 0. Moreover, it isometrically closure set branching points (taken in any minimal that contains $M$) negligible. also prove R$-tree, every extreme point unit ball element form $(\delta(x...

Gi j(·, y) = 0 on ∂Ω ∀y ∈ Ω, where δik is the Kronecker delta symbol and δy(·) is the Dirac delta function with a unit mass at y. In the scalar case (i.e., when N = 1), the Green’s matrix becomes a real valued function and is usually called the Green’s function. We prove that if Ω has either finite volume or finite width, then there exists a unique Green’s matrix in Ω; see Theorem 2.12. The sam...