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Galois connections and isomorphism of simultaneous ordered relations
Omprakash Atale
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partia…
On some generalized number theoretic functions and Ighachanea-Akkouchia Holder's inequalities
Omprakash Atale
Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities…
Type-(I,II) Interpolations and some asymptotic expansions using Ramanujan's master theorem
Omprakash Atale
The theory of Mellin transform is an incredibly useful tool in evaluating some of the well known results for the zeta function. Ramanujan in his quarterly reports \cite{1} gave a t…
Turán-type inequaities for generalized polygamma function
Omprakash Atale
Inspired by the work of C. Mortici [1] and A. Laforgia et. al [2] we have established some new Turán-type inequalities for k-polygamma function and p-k-polygamma function.
Analytic expressions for some Mellin transforms with their application to prime counting function and interpolation formulas for the zeta function
Omprakash Atale
The aim of our present work here is to present few results in the theory of Mellin transforms using the method that S. Ramanujan used in proving his Master Theorem. Further applica…