A. Goswami

activity

20192025

most citedOn approximately monotone and approximately Hölder functions

3 citations · 3 across the 10 of their papers we have counts for

collaborators

11 papers

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.CA2024

Revisiting Fekete's Lemma, Subadditive and Periodic Sequences

Angshuman R. Goswami

In this paper, we present an alternative proof of Fekete's Lemma. We demonstrate that for any subadditive sequence, it is possible to construct a subadditive function that exactly…

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.MG2024

Convex Sequence and Convex Polygon

Angshuman Robin Goswami, István Szalkai

In this paper, we deal with the question; under what conditions the points $P_{i} (x i, y i)$ $(i = 1, \dots, n)$ form a convex polygon provided $x_{1} < \dots < x_{n}$ holds. One of the ma…

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…

math.CA2020

On approximately convex and affine functions

Angshuman R. Goswami, Zsolt Páles

A real valued function $f$ defined on a real open interval $I$ is called $Φ$ -convex if, for all $x, y \in I$ , $t \in [0, 1]$ it satisfies $$ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)+tΦ\big((1-t…

math.CA2020

Characterization of approximately monotone and approximately Hölder functions

Angshuman R. Goswami, Zsolt Páles

A real valued function $f$ defined on a real open interval $I$ is called $Φ$ -monotone if, for all $x, y \in I$ with $x \leq y$ it satisfies $f (x) \leq f (y) + Φ (y - x),$ where $Φ:[0,\el…

math.CA2019★ 3 cited

On approximately monotone and approximately Hölder functions

Angshuman R. Goswami, Zsolt Páles

A real valued function $f$ defined on a real open interval $I$ is called $Φ$ -monotone if, for all $x, y \in I$ with $x \leq y$ it satisfies $f (x) \leq f (y) + Φ (y - x),$ where $Φ:[0,\el…