and Applied Analysis 3 But this fails; for example, let us consider the nonexpansive mapping T : R → R defined by Tx −x for all x ∈ R. It is clear that Fix T {0} and 〈x − Tx, x − q〉 2x2 /≥ 4x2 ‖x − Tx‖2. Recall the following identities in a Hilbert space H: for x, y ∈ H, ω ∈ 0, 1 i ‖x y‖2 ‖x‖2 2〈x, y〉 ‖y‖2; ii ‖ 1 −ω x ωy‖2 1 −ω ‖x‖2 ω‖y‖2 − 1 −ω ω‖x − y‖2. The correction of Maingé’s result is ...

in this paper, we use the concept of graph convergence of h(.,.)-co-accretive mapping introduced by [r. ahmad, m. akram, m. dilshad, graph convergence for the h(.,.)-co-accretive mapping with an application, bull. malays. math. sci. soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...

Abstract. We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Our lower bounds are asymptotically precise at x = 0, while the upper bounds are either asymptotically precise or at least agree with q+1Fq((aq+1), (bq);−x) at x = ∞. Inequalities are derived as corollaries of a theorem asserting the monotony...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

and Applied Analysis 3 for all x, y ∈ C, where cn max{0, supx,y∈C ‖Tnx − Tny‖ − ‖x − y‖ } so that limn→∞cn 0. Hence, T is a generalized asymptotically nonexpansive mapping. The mapping T : C → C is said to be demiclosed at 0 if for each sequence {xn} in C converging weakly to x and {Txn} converging strongly to 0, we have Tx 0. A Banach space E is said to satisfy Opial’s property, see 4 , if for...

Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...