$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...

let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

for sets of sequences x = (xk) which are strongly (V ,λ)-summable to L, that is, xk → L[V,λ]. We recall that a modulus f is a function from [0,∞) to [0,∞) such that (i) f(x)= 0 if and only if x = 0; (ii) f(x+y)≤ f(x)+f(y) for all x, y ≥ 0; (iii) f is increasing; (iv) f is continuous from the right at 0. It follows that f must be continuous on [0,∞). A modulus may be bounded or unbounded. Maddox...

Let G be an algebraic group defined over a field k. We call g ∈ G real if g is conjugate to g−1 and g ∈ G(k) as k-real if g is real in G(k). An element g ∈ G is strongly real if ∃h ∈ G, h2 = 1 (i.e. h is an involution) such that hgh−1 = g−1. Clearly, strongly real elements are real and are product of two involutions. Let G be a connected adjoint semisimple group over a perfect field k, with −1 ...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M . For α > 0, F is α-bounded if Pα(F ) < ∞ where Pα is the α-packing entropy of F introduced in [7]. We say that M is strongly 1-bounded if M has a 1-bounded finite set of selfadjoint generators F such that there exists an x ∈ F with χ(x) > −∞. It is shown that if M is strongly 1-bounded, then any finite set of ...

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d&apos;subseteq m$ such that $n+d&apos;$ is a strongly dense submodule of $m$...