In this article, we established a new version of generalized fractional Hadamard and Fejér–Hadamard type integral inequalities. A operator (FIO) with non-singular function (multi-index Bessel function) as its kernel monotone increasing functions is utilized to obtain the such Our derived results are form several proven inequalities already existing in literature. The useful for studying stabili...

Consider a compact embedded hypersurface ? t in R n+1 which moves with speed determined at each point by a function F (1 ; : : : ; n ; t) of its principal curvatures, for 0 t < T: We assume the problem is degenerate parabolic, that is, that F (; t) is nondecreasing in each of the principal curvatures 1 ; : : : ; n : We shall show that for t > 0 the hypersurface ? t sat-isses local a priori Lips...

in this article, the modified exp-function method is used to construct many exact solutions to the nonlineargeneralized k(n,n) and bbm equations with variable coefficients. under different parameter conditions, explicitformulas for some new exact solutions are successfully obtained. the proposed solutions are found to beimportant for the explanation of some practical physical problems.

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form F + ∑i=1Gi, where F has a Lipschitzcontinuous gradient and the Gi’s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than n = 1 non-smooth function, our method generalizes it to the cas...

In this paper we extend to the vector case the notion of increasing along rays function. The proposed definition is given by means of a nonlinear scalarization through the so-called oriented distance function from a point to a set. We prove that the considered class of functions enjoys properties similar to those holding in the scalar case, with regard to optimization problems, relations with (...

Shamos [1] recently showed that the diameter of a convex n-sided polygon could be computed in O(n) time using a very elegant and simple procedure which resembles rotating a set of calipers around the polygon once. In this paper we show that this simple idea can be generalized in two ways: several sets of calipers can be used simultaneously on one convex polygon, or one set of calipers can be us...

Abstract Fractional calculus operators play a very important role in generalizing concepts of used diverse fields science. In this paper, we use Riemann–Liouville fractional integrals to establish generalized identities, which are further applied obtain midpoint and trapezoidal inequalities for convex function with respect strictly monotone function. These reproduce convex, harmonic p -convex, ...

Generalized linear models (GLMs) represent a popular choice for the probabilistic characterization of neural spike responses. While GLMs are attractive for their computational tractability, they also impose strong assumptions and thus only allow for a limited range of stimulus-response relationships to be discovered. Alternative approaches exist that make only very weak assumptions but scale po...

Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets. The simultaneous multiprojection algorithm of Censor and Elfving for solving the CFP,...