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Harikrishnan P K

Harikrishnan P K
Manipal Academy of Higher Education (Deemed to be University) · Mathematics

MSc, BEd, Ph.D

About

24
Publications
1,810
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64
Citations
Additional affiliations
November 2010 - February 2015
Manipal Academy of Higher Education
Position
  • Professor (Assistant)

Publications

Publications (24)
Article
Full-text available
The idea of convex sets and various related results in 2-Probabilistic normed spaces were established in [7]. In this paper, we obtain the concepts of convex series closedness, convex series compactness, boundedness and their interrelationships in Menger’s 2-probabilistic normed space. Finally, the idea of D- Boundedness in Menger’s 2-probabilistic...
Article
Let N be a zero-symmetric (right) nearring with identity. We introduce a partial order in the matrix nearring corresponding to the partial order (defined by Pilz in Near-rings: the theory and its applications, North Holland, Amsterdam, 1983) in N . A positive cone in a matrix nearring is defined and a characterization theorem is obtained. For a con...
Article
In this paper, we have introduced the notions of strong and weak convergences in 2-probabilistic normed spaces (2-PN spaces) and established some of its properties. Later, we have defined the strong and weak boundedness of a linear map between two 2-PN spaces and proved a necessary and sufficient condition for the linear map between two 2-PN spaces...
Article
Let $G$ be an $N$-group where $N$ is a (right) nearring. We introduce the concept of relative essential ideal (or $N$-subgroup) as a generalization of the concept of essential submodule of a module over a ring or a nearring. We provide suitable examples to distinguish the notions relative essential and essential ideals. We prove the important prope...
Article
We introduce the concept of essentiality in a lattice [Formula: see text] with respect to an element [Formula: see text]. We define notions such as [Formula: see text]-essential, [Formula: see text]-uniform elements and obtain some of their properties. Examples of lattices are given wherein essentiality can be retained with respect to an arbitrary...
Article
The study of semi bent functions (2- plateaued Boolean function) has attracted the attention of many researchers due to their cryptographic and combinatorial properties. In this paper, we have given the algebraic construction of semi bent functions defined over the finite field F_2^n (n even) using the notion of trace function and Gold power expone...
Article
Near-bent functions that occur in odd dimensions are the important class of Boolean functions, which are useful functions for cryptography. In this paper, we construct near-bent function with trace term using well known Welch function exponent in polynomial form and various other forms of near-bent functions. We have also investigated some importan...
Article
Full-text available
Remark 4.1 and Remark 4.5 in Section 4 will be true only if a is a power of two.
Article
Full-text available
Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functio...
Preprint
In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if $A\in \mathbb{B}\left( \mathcal{H} \right)$ and $r\ge 2$, then \[{{w}^{r}}\left( A \right)\le {{\left\| A \right\...
Article
Full-text available
In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if A ∈ B (H) and r ≥ 2, then w r (A) ≤ A r − inf x=1 ||A| − w (A)| r 2 x 2 where w (·) and ·· denote the numerical r...
Article
Full-text available
In this paper, we obtain some properties of invertible operators; convex, balanced, absorbing sets; and D-boundedness in Šerstnev spaces. We prove that some PN spaces (V,ν,τ,τ∗), which are not Šerstnev spaces, in which the triangle function τ∗ is not Archimedean can be endowed with a structure of a topological vector space, and we give suitable exa...
Book
Full-text available
This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approxima...
Article
In this paper we introduce the concept of accretive opera- tors, discuss some properties of resolvents of an accretive operator in 2- probabilistic normed spaces and focusing on the results of convex sets in 2-probabilistic normed spaces.
Article
Full-text available
In this paper we introduce the concept of accretive operator in linear 2-normed spaces, focusing on the relationships and the various aspects of accretive, m-accretive and maximal accretive operators. We prove the analogous of Banach-Alaoglu theorem in linear 2- normed spaces, obtaining an equivalent definition for accretive operators in linear 2-n...
Article
Full-text available
In this paper we discuss some properties of resolvents of an accretive operator in linear 2-normed spaces, focusing on the concept of contrac- tion mapping and the unique fixed point of contraction mappings in linear 2- normed spaces. Also, we establish the existence of solution of strong accretive operator equation in linear 2-normed spaces
Article
Full-text available
In this paper we describe the proof of 'Riesz Theorems' in 2- inner product spaces. The main result holds only for a b-linear functional but not for a bilinear functional.
Article
We are defining the conjugate of an element in a C* algebra and a conjugate space, also studying its properties in detail.

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