We present a realization for some K-functionals associated with Jacobi expansions in terms of generalized Jacobi-Weierstrass operators. Fractional powers of the operators as well as results concerning simultaneous approximation and Nikolskii-Stechkin type inequalities are also considered.
The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m), and it is denoted by . Estimating covering functionals of convex bodies is an important part of Chuanming Zong's quantitative program for attacking Hadwiger's covering conjecture. Estimations of covering functionals of cones and double cones, which are best possible for certain pairs of m and K, are presented.
The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results. The effectiveness of the obtained criteria is illustrated via examples.
In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem. We introduce a new method of an iterative scheme for finding a common element of the set of solutions of variational inequality problems and the set of common fixed points of a finite family of quasi-nonexpansive mappings and the set of solutions of the modified split generalized equilibrium problem without assuming a demicloseness condition and , where T is a quasi-nonexpansive mapping and ; a difficult proof in the framework of Hilbert space. In addition, we give a numerical example to support our main result.
The purpose of this paper is to derive some Coifman type inequalities for the fractional convolution operator applied to differential forms. The Lipschitz norm and BMO norm estimates for this integral type operator acting on differential forms are also obtained.
In this paper, we introduce the sequence spaces , , and . We investigate some functional properties, inclusion relations, and the α-, β-, γ-, and continuous duals of these sets.
In this paper, we refine and generalize some weighted arithmetic-geometric operator mean inequalities due to Lin (Stud. Math. 215:187-194, 2013) and Zhang (Banach J. Math. Anal. 9:166-172, 2015) as follows: Let A and B be positive operators. If or , then for a positive unital linear map Φ,
In this paper, we give asymptotic expansions and inequalities related to the generalized Somos quadratic recurrence constant, using its relation with the generalized Euler constant.
In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschitl type approximation formulas have good properties, such as monotonicity and convexity. These not only yield some new inequalities for the gamma and factorial functions, but also provide a new proof of known inequalities and strengthen known results.
The aim of present work is to study some kinds of well-posedness for a class of generalized variational-hemivariational inequality problems involving set-valued operators. Some systematic approaches are presented to establish some equivalence theorems between several classes of well-posedness for the inequality problems and some corresponding metric characterizations, which generalize many known results. Finally, the well-posedness for a class of generalized mixed equilibrium problems is also considered.
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