Càdlàg Functions

This chapter considers the space D of functions on the unit interval that are continuous on the right and with left limits, known as càdlàg functions. D contains and extends the space C, but is nonseparable under the uniform metric so to work with it calls for new techniques. By defining a new topology for D (the Skorokhod topology), families of measures on D can be constructed and sufficient conditions for weak convergence of partial sum processes specified.

A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum

In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.

Pascu-Type Analytic Functions by Using Mittag-Leffler Functions in Janowski Domain

Keeping in view the various important applications of Mittag-Leffer functions in the fields of applied sciences, we introduce Pascu-type analytic functions utilizing the concept of Mittag-Leffler functions in the region of Janowski domain. Moreover, we investigate some useful properties of these functions such as sufficiency criteria, distortion and growth bounds, convex combination, radius of starlikeness, and some partial sum results.

Partial sum of the products of the Horadam numbers with subscripts in arithmetic progression

We evaluate the partial sum of the products of the terms of any two Horadam sequences with subscripts in arithmetic progression. Illustrative examples are drawn from six well-known Horadam sequences.

Does Crude Oil Price Affect the Inflation Rate and Economic Growth in India? A New Insight Based on Structural VAR Framework

Based on a structural vector autoregressive framework on the monthly data from April 1997 to July 2016, this study is an attempt to show the impact of crude oil price on the rate of inflation and economic growth in India. The results showed that the crude oil price has a positive impact on the rate of inflation whereas an inverse relation exists between crude oil price and economic growth. Further, we segregated the crude oil price into two components, that is, positive and negative partial sum of oil price through the nonlinear and asymmetric autoregressive distribution lag framework. A similar kind of result is derived in the case of positive partial sum of oil price on the rate of inflation and economic growth, while a significant negative relationship is found in the negative partial sum of crude oil price on economic growth. From the policy perceptive, we suggest that policymakers may focus on reducing the consumption of crude oil and using renewable energy for accelerating the economic growth. This would not only prevent the domestic economy from international oil price fluctuations and inflation but also assist in achieving sustainable environmental goal of reduced crude oil use. JEL Classification Codes: C3, O4, Q4