This article gives a really vital and curiously inequality on Jain-Saraswat’s functional discrimination in terms of the Hellinger Bhattacharya by taking into thoughtL-Lipschitzian functions. Encourage, we outlined few results utilizing inferred with numerical confirmation.

The metabolism of r-lactate and pyruvate, labeled uniformly with 14C, by epididymal fat pad tissue of fasted and fasted-refed rats was studied. In tissue of fasted-refed rats, pyruvate and L-lactate were utilized at equal rates. L-Lactate was nearly all converted into CO2 and fatty acids, and pyruvate into COZ, fatty acids, and L-lactate. The incorporation of 14C into glycerol was very low. L-L...

We consider some typical optimal control problems for a nonlinear model of longitudinal vibrations in a viscoelastic rod. In trying to follow the usual pattern of showing that every innmizing sequence of controls contains a subsequence suitably converging to an optimal control, we confront the severe technical diiculty that the constitutive function cannot be uniformly Lipschitzian in its argum...

In this work we introduce for extended real valued functions, defined on a Banach space X, the concept of K directionally Lipschitzian behavior, where K is a bounded subset of X. For different types of sets K (e.g., zero, singleton, or compact), the K directionally Lipschitzian behavior recovers well-known concepts in variational analysis (locally Lipschitzian, directionally Lipschitzian, or co...

We prove that any weak space-time L vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of R satisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove that t − a.e. weak L inviscid limits of solutions of 3D Navier-Stokes equations in bounded domains are weak solutions of the Euler equation if they...

Let C be a nonempty closed convex subset of a real Banach space E. Let S : C → C be a quasi-nonexpansive mapping, let T : C → C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F := {x ∈ C : Sx = x and Tx = x} 6 = ∅. Let {xn}n≥0 be the sequence generated from an arbitrary x0 ∈ C by xn+1 = (1− cn)Sxn + cnT xn, n ≥ 0. We prove necessary and sufficient conditions fo...

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., `p, 1 < p < ∞). Let T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K of E and let ω ∈ K be arbitrary. Then the iteration sequence {zn} defined by z0 ∈ K, zn+1 = (1 − μn+1)ω + μn+1yn; yn = (1 − αn)zn + αnTzn, converges strongly to a fixed poi...

Abstract In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote variational inequality problem, general system of inequalities, hierarchical inequality, common fixed-point problem countable family uniformly Lipschitzian pseudocontractive mappings an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-s...

A weak e-net for a set of points M, is a set of points W (not necessarily in M) where every convex set containing eiMI points in M must contain at least one point in W. Weak e-nets have applications in diverse areas such as computational geometry, learning theory, optimization and statistics. Here we show that, if M is a set of points quasi-uniformly distributed on a unit sphere sd-l, then ther...