Based on a common article of the authors, we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another set-valued maximally monotone operator. Depending on the nature of the single-valued operator, we propose two iterative penalty ...

In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint Splitting (AFBA), for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical operator splitting methods, like DouglasRachford (DRS) and Forward-Backward splitting (FBS) are special cases of our new algorithm. Among other things, AF...

*Correspondence: [email protected] 3Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran Full list of author information is available at the end of the article Abstract In this paper, we introduce and consider a new system of generalized nonlinear mixed variational inequalities involving six different nonlinear operators and discuss the existence and uniqueness of s...

A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize thei...

A common and useful technique to simplify some problems given in a metric space (V, d) is to approximate the metric with a simpler metric. An exact embedding of a metric space (V, d) into another metric space (V , d) is a mapping f : V → V ′ such that for all x, y ∈ V , d(x, y) = d(f(x), f(y)). Typically we cannot get an exact embedding and we settle for embeddings that preserve the distances a...

Let k be an integer, k ≥ 3, and let Zk be the cyclic group of order k. Take λk ∈ [k+2,∞) to be the smallest integer such that for every λk-edge-connected graph G and every mapping f : V (G) → Zk with |E(G)| k ≡ ∑ v∈V (G) f(v), there exits an orientation for G such that for each vertex v, d G (v) k ≡ f(v), where d G (v) denotes the out-degree of v. Lovász, Thomassen, Wu, and Zhang (2013) proved ...