On the Schwab-Borchardt mean.
On the Schwab-Borchardt mean. II.
On the shift-window phenomenon of super-functions.
On Zeros of Polynomials of Best Approximation to Holomorphic and C... Functions.
Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications
We extend the open mapping theorem and inversion theorem of Robinson for convex multivalued mappings to γ-paraconvex multivalued mappings. Some questions posed by Rolewicz are also investigated. Our results are applied to obtain a generalization of the Farkas lemma for γ-paraconvex multivalued mappings.
Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Optimal inequalities among various means of two arguments.
Optimal inequalities for generalized logarithmic, arithmetic, and geometric means.
Optimal power mean bounds for the weighted geometric mean of classical means.
Optimal sublinear inequalities involving geometric and power means
There are many relations involving the geometric means and power means for positive -vectors . Some of them assume the form of inequalities involving parameters. There then is the question of sharpness, which is quite difficult in general. In this paper we are concerned with inequalities of the form and with parameters and We obtain a necessary and sufficient condition for the former inequality, and a sharp condition for the latter. Several applications of our results are also demonstrated....
Optimal weighted harmonic interpolations between Seiffert means
We provide a set of optimal estimates of the form (1-μ)/𝓐(x,y) + μ/ℳ (x,y) ≤ 1/ℬ(x,y) ≤ (1-ν)/𝓐(x,y) + ν/ℳ (x,y) where 𝓐 < ℬ are two of the Seiffert means L,P,M,T, while ℳ is another mean greater than the two.
Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.
Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).
Ostrowski inequalities on time scales.
P-adic continuously differentiable functions of several variables.
Parametrization of Carathéodory multifunctions
Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions
We consider a multifunction , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
Peano type theorem for random fuzzy initial value problem
In this paper we consider the random fuzzy differential equations and show their application by an example. Under suitable conditions the Peano type theorem on existence of solutions is proved. For our purposes, a notion of ε-solution is exploited.
Periodic oscillation of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients.
Periodicity, almost periodicity for time scales and related functions
In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.
Polynomial inequalities on general subsets of