In [10], for continuous functions f from the domain of certain discrete operators Ln the inequalities are proved concerning the modulus of continuity of Lnf . Here we present analogues of the results obtained for the Durrmeyer-type modification ̃ Ln of Ln. Moreover, we give the estimates of the rate of convergence of ̃ Lnf in Hölder-type norms

*Correspondence: [email protected] 1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India 2Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract The aim of this paper is to intro...

We present some sufficient conditions for which a Banach space X has normal structure in terms of the modulus of U-convexity, modulus of W∗-convexity, and the coefficient R 1, X , which generalized some well-known results. Furthermore the relationship between modulus of convexity, modulus of smoothness, and Gao’s constant is considered, meanwhile the exact value of Milman modulus has been obtai...

A sufficient condition for the uniform modulus of continuity of a random field X = {X(t), t ∈ RN} is provided. The result is applicable to random fields with heavy-tailed distribution such as stable random fields. Running head: Uniform Modulus of Continuity of Random Fields 2000 AMS Classification numbers: 60G60, 60G52, 60G17, 60G18.

This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L2 modulus of continuity for a one-dimensional Brownian motion. (c) Extens...

Abstract. This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on 3 closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L modulus of continuity for a 1-dimensional Brownian motion. (c) Ext...

The aim of the present paper is to introduce new type integral operators which involve Sheffer polynomials. We investigate approximation properties of the our operators with the help of the universal Korovkin-type property and also establish the rate of convergence by using modulus of continuity, second order modulus of smoothness and Petree’s Kfunctional. Moreover, some examples which include ...