A. Goswami

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20192025

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math.GM2025

On Characterizations of Convex and Approximately Subadditive Sequences

Angshuman Robin Goswami

A sequence $(u_{n})_{n = 0}^{\infty}$ is said to be convex if it satisfies the following inequality $$ 2u_n\leq u_{n-1}+u_{n+1}\qquad \mbox{for all}\qquad n\in\mathbb{N}. $$ We…

math.GM2024

On approximately Convex and Affine Sequences

Angshuman Robin Goswami

In this paper, our primary objective is to study a possible decomposition of an approximately convex sequence. For a given $ε > 0$ ; a sequence $\big<u_n\big>_{n=0}^{\infty}…

math.GM2024

Decomposition of Approximately Monotone and Convex Sequences

Angshuman Robin Goswami

In this paper, we primarily deal with approximately monotone and convex sequences. We start by showing that any sequence can be expressed as the difference between two nondecreasin…

math.GM2023

Hermite-Hadamard type inequalities by using Newton-Cotes quadrature formulas

Angshuman R. Goswami, Ferenc Hartung

A convex function $f : [a, b] \to R$ satisfies the so-called Hermite-Hadamard inequality $$ f\left(\frac{a+b}{2}\right)\leq \frac{1}{b-a}\int_a^{b}f(t)dt\leq \frac{f(a)+f(b)}{2…

math.GM2023

Generalization of Subadditive, Monotone and Convex Functions

Angshuman R. Goswami

Let $I \subseteq R_{+}$ be a non empty and non singleton interval where $R_{+}$ denotes the set of all non negative numbers. A function $Φ : I \to R_{+}$ is…

math.GM2023

Generalizing the Concept of Bounded Variation

Angshuman R. Goswami

Let $[a, b] \subset R$ be a non empty and non singleton closed interval and $P = {a = x_{0} < \dots < x_{n} = b}$ is a partition of it. Then $f : I \to R$ is said to be a function…