P. D. Srivastava

Indian Institute of Technology Kharagpur | IIT KGP · Department of Mathematics

The inĄnite lower triangular matrix B(r1, . . . , rl ; s1, . . . , sl ′ ) is considered over the sequence space c0, where l and l ′ are positive integers. The diagonal and sub-diagonal entries of the matrix consist of the oscillatory sequences r = (rk(mod l)+1) and s = (sk(mod l ′)+1), respectively. The rest of the entries of the matrix are zero. I...

Patra, ArnabShrivastava, AmitSharma, RohitSrivastava, P. D.If two quantum states are unitarily equivalent then their von Neumann entropies are same. Converse statement also holds, which was proved by Kan He et al. [Applied Mathematics Letters, 2012;25(8):1391–1393 [1]]. In this paper, we extend it to bipartite quantum system and prove a sufficient...

The infinite lower triangular matrix B(r_1,...,r_l ; s_1,...,s_l') is considered over the sequence space c_0 , where l and l' are positive integers. The diagonal and sub-diagonal entries of the matrix consist of the oscillatory sequences r = (r_k(mod l)+1) and s = (s_k(mod l')+1), respectively. The rest of the entries of the matrix are zero. It is...

The present article is a continuation of the work done by Birbonshi and Srivastava (Complex Anal Oper Theory 11:739–753, 2017) where the authors obtained the spectrum and fine spectrum of banded triangular matrices such that the entries of each band are constant. In this article, we consider the same problem for triangular band matrices such that e...

In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the [Formula: see text]-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric calculus which is analogous to the classical Hermite interpolating polynomial.

The spectrum of triangular band matrices defined on the sequence spaces where the entries of each band are a constant or convergent sequence is well studied. In this article, the spectrum and fine spectrum of a new generalized difference operator defined by a lower triangular triple band matrix on the sequence space (Formula presented.) are obtaine...

In this paper, we have obtained some conditions under which the boundary of the numerical range of tridiagonal matrices has no point spectrum. As a consequence of these results, the boundary of the numerical range of these tridiagonal matrices may be non-round only at the points where it touches the essential spectrum.

The spectrum of triangular band matrices defined on the sequence spaces where the entries of each band is a constant or convergent sequence is well studied. In this article, the spectrum and fine spectrum of a new generalised difference operator defined by a lower triangular triple band matrix on the sequence space $l_p (1 \leq p < \infty)$ are obt...

In this paper, using m-th order difference operator ∆(m) and a sequence {αn}∞n=0 of strictly positive real numbers, sequence spaces (Formula Presented) are introduced, where (Formula Presented) are sequence of Orlicz functions. It is shown that these are separablen=0,Banach spaces and dense Fσ-set of the first Baire category in s, the space of all...

In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the $\alpha$-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric calculus which is analogous to the classical Hermite interpolating polynomial.

In this paper, some new relative perturbation bounds for the eigenvalues of diagonalizable matrices are derived. A relative perturbation bound for singular values is also obtained. The present results improve some existing results.

In this paper, we determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the generalized difference operator $\Delta_{a,b}$ on the sequence space $\ell_p \ (1< p < \infty)$ where the real sequences $a=\{a_k\}$ and $b=\{b_k\}$ are not necessarily convergent. Hence our results generalize the work given by Akh...

In this paper, we generalize the fractional order difference operator using $l$- Pochhammer symbol and define $l$- fractional difference operator. The $l$- fractional difference operator is further used to introduce a class of difference sequence spaces. Some topological properties and duals of the newly defined spaces are studied.

The spectra and fine spectra of the lower triangular matrix $\mathbb{B}$ $(r_1,\dots , r_l;$ $ s_1, \dots, s_{l'})$ over the sequence space $c_0$ are determined. The diagonal and sub-diagonal entries of the matrix consist of two oscillatory sequences $r=(r_{k (\text{mod} \ l)+1})$ and $s= (s_{k(\text{mod} \ l')+1})$ respectively, whereas the rest o...

In this paper, we investigate the geometric property $(k$-$\beta)$ for any fixed integer $k\geq 1$ of the space $l_\Phi((E_{n}))$ generated by a Musielak-Orlicz function $\Phi$ and a sequence $(E_n)$ of finite dimensional spaces $E_{n}$, $n\in \mathbb{N}$, equipped with both the Luxemburg and the Amemiya norm. As a consequence, we obtain the proper...

User’s password with smart card based authentication protocol is needed to access resources securely from remote server. In 2014, Huang et al. proposed a timestamp-based authentication protocol and they claimed that their scheme is secure against all possible attacks. In this paper, we have pointed out that Huang et al.’s scheme is insecure against...

Anderson's theorem states that if the numerical range W(A) of an n-by-n matrix A is contained in the unit disk and intersects with the unit circle at more than n points, then it coincides with the (closed) unit dissk. An analogue of this result for compact A in an infinite dimensional setting was established by Gau and Wu. We consider here the case...

Anderson's theorem states that if the numerical range W(A) of an n-by-n matrix A is contained in the unit disk and intersects with the unit circle at more than n points, then it coincides with the (closed) unit dissk. An analogue of this result for compact A in an infinite dimensional setting was established by Gau and Wu. We consider here the case...

The purpose of this paper is to determine spectrum and fine spectrum of newly introduced operator Δuvw2 on sequence space l1. The operator Δuvw2 on sequence space l1 is defined by Δuvw2x=(unxn+vn-1xn-1+wn-2xn-2)n=0∞ with x−1, x−2 = 0, where x = (xn) ∈ l1, u = (uk) is either constant or strictly increasing sequence of positive real numbers with U=li...

In this paper some necessary and sufficient conditions for boundedness of an infinite matrix as a linear operator between two weighted \(c_0\) spaces are established. Some relationship between the matrix and the weight vectors of domain and range spaces are also obtained.

It has been observed that for the 2nd and 3rd band lower triangular matrices $B(r,s)$ and $B(r,s,t)$, only the boundary of the spectrum gives the continuous spectrum while the rest of the entire interior region gives the residual spectrum over the sequence spaces $c_0$, $l_p$ and $bv_p$. The main focus of our present study is to investigate the pos...

In this paper, we study the numerical range of Jacobi operators and it is shown that under certain conditions, the boundary of the numerical range of these operators can be non-round only at the points where it touches the essential spectrum. It is further shown that these points cannot be the eigenvalue of the Jacobi operators.

It has been observed that for the 2nd and 3rd band lower triangular matrices $B(r,s)$ and $B(r,s,t)$, only the boundary of the spectrum gives the continuous spectrum while the rest of the entire interior region gives the residual spectrum over the sequence spaces $c_0$, $l_p$ and $bv_p$. The main focus of our present study is to investigate the pos...

The cluster heads in hierarchical wireless sensor networks gather real time data from the other ordinary sensor nodes and send those data to a nearest base station. But, the main important issue is that how a user will get the real time data directly from a cluster head se- curely. To solve this problem, many user authentication schemes have been p...

The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found some suitable conditions to get its relation with the generalized statistical convergence. Finally we have pro...

In this paper, We have introduced a new class of sequences of fuzzy numbers defined by using modulus function and generalized weighted mean over the class defined in \cite{OS}. We have proved that this class form a quasilinear complete metric space under a suitable metric. Various inclusion relations and some properties such as solidness, symmetry...

This paper presents new sequence spaces $X(r, s, t, p ;\Delta)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete under a suitable paranorm. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also obtaine...

The class bvF(u,v) of bounded variation sequences of fuzzy numbers, introduced by Ojha and Srivastava (2015), has been investigated further using generalized weighted mean matrix G(u, v). On imposing certain restrictions on the matrix G(u, v), we have established its relation with different class of sequences of fuzzy numbers such as statistically...

The class of bounded variation $bv^F(u,v)$ of fuzzy numbers introduced by [8] has been investigated further with the help of the generalized weighted mean matrix $G(u,v)$. Imposing some restrictions on the matrix $G(u,v)$, we have established it's relation with different class of sequences such as our known classical sets, set of all statistically...

Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $\alpha\beta$ - statistical convergence of order $\theta$ in case of fuzzy functions and classified it into pointwise, uniform and equi-statistical convergence. We have checked some basic properties and then the convergence are investigat...

Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $\alpha\beta$ - statistical convergence of order $\theta$ in case of fuzzy functions and classified it into pointwise, uniform and equi-statistical convergence. We have checked some basic properties and then the convergence are investigat...

We have introduced a new sequence space l(r, s, t, p;Δ(m)) combining by using generalized means and difference operator of order m. Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the α-, β-, γ- duals of this space are computed and also obta...

Necessary and sufficient conditions for the non-triviality of a Musielak-Orlicz sequence space V Φ (λ) generated by the de la Vallée-Poussin means are obtained. Topological properties such as completeness, separability, order continuity are characterized for the space V Φ (λ). Finally, criteria for the coordinatewise uniformly Kadec-Klee property a...

It is not always possible for a patient to go to a doctor in critical or urgent period. Telecare Medical Information Systems (TMIS) provides a facility by which a patient can communicate to a doctor through a medical server via internet from home. To hide the secret information of both parties (a server and a patient), an authentication mechanism i...

A generalized Cesàro-Musielak-Orlicz sequence space Ces_Φ(q) endowed with the Amemiya norm is introduced. Criteria for the coordinatewise uniformly Kadec-Klee property and the uniform Opial property of the space Ces_Φ(q) with respect to the Amemiya norm are obtained.

In this paper we have introduced a new sequence ideal using Orlicz function and the notion of de la Vallée Poussin mean. It is proved that the Cesáro-Orlicz sequence ideal is complete under a suitable norm. Moreover, it is shown that Cesáro-Orlicz sequence ideal is maximal, and if the Orlicz function satisfies Δ2Δ2-condition at zero then it is also...

Let $\bold{\Phi}=(\phi_n)$ be a Musielak-Orlicz function, $X$ be a real Banach space and $A$ be any infinite matrix. In this paper, a generalized vector-valued Musielak-Orlicz sequence space $l_{\bold {\Phi}}^{A}(X)$ is introduced. It is shown that the space is complete normed linear space under certain conditions on the matrix $A$. It is also show...

A generalized Cesàro–Musielak–Orlicz sequence space CesΦ(q) equipped with the Luxemberg norm is introduced. It is proved that CesΦ(q) is a Banach space and also criteria for the coordinatewise uniformly Kadec–Klee property and the uniform Opial property are obtained.

In this paper, we have introduced a sequence space \(l_p(r,s, t; B^{(m)})\), \(1\le p< \infty \) and proved that the space is a complete normed linear space. We have also shown that the space \(l_p(r,s, t; B^{(m)})\) is linearly isomorphic to \(l_p\) for \(1\le p< \infty \). Further, we have established some identities or estimates for the operator...

In this paper, sequence spaces X(r,s,t;B(m)) for X∈{l∞,c,c0} are introduced by combining the generalized means and the m-th order generalized difference operator B(m)(u,v). It is shown that these spaces are complete normed linear spaces and the spaces c0(r,s,t;B(m)), c(r,s,t;B(m)) have Schauder bases. Furthermore, the α-, β-, γ-duals of these space...

Let s = (sn) be a sequence of s-numbers in the sense of Pietsch and A be an infinite matrix. This paper presents a generalized class A(s) - p of s-type | A, p | operators using s-number sequence which unifies many earlier well known classes. It is shown that the class A(s) - p forms a quasi-Banach operator ideal under certain conditions on the matr...

A sufficient condition for Musielak-Orlicz sequence space V Φ (λ) defined by de la Vallée-Poussin means to be (k-NUC), k≥2 is obtained. Under certain assumptions on φ-functions, it is shown that the modular space X σ s is a Fréchet space and the modular spaces X σ ^ for σ ^=σ w μ ,σ q Q , σ 0 are identical as sets.

In this paper, we introduce the space of lacunary strongly Δ (p) m -summable sequences of fuzzy numbers and discuss relations between Δ m -statistically convergent sequences and lacunary Δ m -statistically convergent sequences of fuzzy numbers. We also study inclusion relations using different arbitrary lacunary sequences.

In this paper, we introduce and study the concept of Δ m -summable sequence of fuzzy numbers by using a modulus function and Δ m -statistical convergence of sequences fuzzy numbers. Also we have defined Δ m -statistical pre-Cauchy sequences of fuzzy numbers.

In this paper, we introduce the concept of λ-statistical convergence of order θ and strong λ-summability of order θ for the sequence of fuzzy numbers. Further the same concept is extended to the sequence of fuzzy functions and introduce the spaces like (Formula presented) and (Formula presented). Some inclusion relations in those spaces and also th...

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is compute...

A difference sequence space using φ-function and involving the concept of de la Vallée-Poussin mean is introduced. Inclusion relations, structural and topological properties of this space are investigated. By introducing a modular structure, the equality of the countably and uniformly countably modulared spaces is obtained.

This paper presents new sequence spaces $X(r, s, t, p ; B)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the spaces $X(r, s, t, p ; B)$ for $X \in \{c(p), c_0(p), l(p)\}$ have Schauder basis. Furthermore, the $\alpha$-, $\...

In this paper, new sequence spaces $X(r, s, t ;\Delta^{(m)})$ for $X\in \{l_\infty, c, c_0\}$ defined by using generalized means and difference operator of order $m$ are introduced. It is shown that these spaces are complete normed linear spaces and the spaces $c_0(r, s, t ;\Delta^{(m)})$, $c(r, s, t ;\Delta^{(m)})$ have Schauder basis. Furthermore...

In this article, we have defined the remainder form of the sequential ?-modulus using ?-function by introducing the notion of second order modulus of smoothness for sequences. Structural properties of sequence spaces generated by means of the sequential ?-moduli are investigated.

In 1975, Rhoades [9] generalized the classes of, operators of lp type and operators of Ces̀aro type by introducing an arbitrary infinite matrix A = (ank) using approximation numbers of a bounded linear operator. In the same paper Rhoades has proved that for each fixed matrix A satisfying the condition |an,2k-1| + |an,2k| = M|ank| on the matrix A =...

Let s=(sn)s=(sn) be a sequence of s-numbers in the sense of Pietsch. In this paper we have introduced a class Ap,q(s) of s-type ces(p,q)ces(p,q) operators by using weighted Cesàro sequence space for 1<p<∞1<p<∞. It is shown that the class Ap,q(s) forms a quasi-Banach operator ideal. Moreover, the inclusion relations among the operator ideals as well...

The purpose of this paper is to determine spectrum and fine spectrum of the operator ∆uv on the sequence space c0. The operator ∆uv on sequence space c0 is defined as ∆uv x = (unxn +vn−1xn−1)∞n=0 satisfying certain conditions, where x−1 = 0 and x = (xn) ∈ c0. In this paper we have obtained the results on the spectrum and point spectrum for the oper...

The purpose of this paper is to determine spectrum and fine spectrum of newly introduced operator Δ 2uv on sequence space c 0. The operator Δ 2uv on sequence space c 0 is defined by Δ 2uvx = (u nx n-v n-1x n-1 + u n-2x n-2) ∞n=0 with x -1, x -2 = 0, where x = (x n) ∈ c 0, u = (u k) is a either constant or strictly decreasing sequence of positive re...

In this paper, we propose a cryptosystem which can encrypt and decrypt long (text) messages in efficient manner. The proposed cryptosystem is a combination of symmetric-key and asymmetric-key cryptography, where asymmetric-key cryptography is used to transmit the secret key to an intended receiver and the sender/receiver encrypts/decrypts messages...

In this paper we introduce a generalized vector-valued paranormed sequence space Np(Ek,Δm,f,s) using modulus function f, where p=(pk) is a bounded sequence of positive real numbers such that infkpk>0,(Ek,qk) is a sequence of seminormed spaces with Ek+1⊆Ek for each k ∈N and s⩾0. We have also studied sequence space Np(Ek,Δm,fr,s), where fr=f∘f∘f∘,…,f...

In this paper, we propose a new security protocol which is styled hierarchical access control-based proxy signature (HACBPS). In hierarchical access control, upper security level users can access some secret information hold by lower security level users, but reverse is not allowed. Whereas in proxy signature, on behalf of the original signer, prox...

The user authentication mechanism is an important part of the network security to protect unauthorized access of a networked system. Based on cryptographic techniques, several schemes have been proposed in the literature for ID-based authentication schemes with smart cards. In 2004, Das et al. propose a scheme for a dynamic ID-based remote user aut...

Digital multisignature is signed by multiple signers with the knowledge of multiple private keys and can be verified based on all signers' public keys. In 2004, Rahul et al. proposed a multisignature scheme for implementing safe delivery rule in group communication systems. In 2005, Das et al. pointed out weaknesses to forgery as well as signature...

In a proxy signature scheme, an original signer delegates his or her signing capability to a proxy signer, and then the proxy signer creates a signature on behalf of the original signer. Proxy signature schemes find applications in a variety of computing environments such as mobile agents for e-commerce, global distribution networks, mobile communi...

Blocking artifact is one of the main drawbacks of the block-based watermarking method. Though a number of researches on ``transparent'' digital watermarking system have been presented, all of them use their own criteria in specific domain such as the discrete cosine transform (DCT), discrete wavelet transform (DWT), etc. In this paper, a generic cr...

In this paper, we introduce a generalized vector valued paranormed double sequence space F2(E, p, f, s), using modulus function f, where p = (pnk) is a sequence of non-negative real numbers, s ≥ 0 and the elements are chosen from a seminormed space (E, qE). Results regarding completeness, normality, K2-space, co-ordinate wise convergence etc. are d...

Digital multisignature is signed by multiple signers with the knowledge of multiple private keys and can be verified based on all signers' public keys. In 2004, Rahul et al. pro- posed a multisignature scheme for implementing safe de- livery rule in group communication systems. In 2005, Das et al. pointed out weaknesses to forgery as well as signa-...

In 1999, Yang and Shieh proposed two authentication schemes with smart cards, one is timestamp-based password authentication scheme and other is nonce-based password authentication scheme. In 2002, Chan and Cheng pointed out that Yang and Shieh’s timestamp-based password authentication scheme is insecure to vulnerable forgery attack. Further, in 2...

In this paper, new classes hN(Ek)hN(Ek), ℓM(B(Ek,Y))ℓM(B(Ek,Y)) and ℓM(Ek′) of vector valued sequences using Örlicz function M are introduced as generalization of known Örlicz sequence spaces hNhN and ℓMℓM, respectively, and Köthe–Töeplitz dual, continuous dual, operator representation and weak convergence for these spaces studied. With different c...

In this paper, new classes , and of vector valued sequences using Örlicz function M are introduced as generalization of known Örlicz sequence spaces and , respectively, and Köthe–Töeplitz dual, continuous dual, operator representation and weak convergence for these spaces studied. With different choice of and M, it is observed that these spaces inc...

We define the idea of statistical convergence and statistically Cauchy sequences over the generalized class of composite vector valued sequence spaces F(E k ,f).

In a hierarchical structure, a user in a security class has access to information items of another class if and only if the former class is a predecessor of latter. Based upon cryptographic techniques, several schemes have been proposed for solving the problem of access control in hierarchical structures. In this paper, we propose a new scheme for...

Recently, Fang et al (24) proposed an improvement to Das et al's scheme (6) to prevent some weaknesses. Further, Chou et al (19) and Thulasi et al (23) pointed out some weak- ness of Das et al's scheme. However, the improvd scheme is still insecure to off-line attack. In this paper, we propose an improvement of their schemes that provides the bette...

The purpose of this paper is to introduce and study some vector valued difference sequence spaces which are defined by combining sequences of Orlicz functions and using the concepts of lacunary convergence and strong A-convergence, where A=(a ik ) is an infinite matrix of complex numbers. We study also some topological properties of these spaces an...

In this paper, we define and study the vector valued sequence space F(Ek,f) using modulus function f. The results of this paper generalize the corresponding results of Maddox 1.

In this paper, we introduced some new sequence space using Orlicz function and study some properties of this space. http://web.math.hr/glasnik/vol_34/no2_12.html

We introduce a general sequence space X v , where X is any sequence space and establish some inclusion relations, topological results. Furthermore we give α- and β-duals of sequence spaces [ℓ(p)] v , [c 0 (p)] v , [ℓ ∞ (p)] v and [c(p)] v together with α-duals of sequence spaces ℓ(p), c 0 (p), ℓ ∞ (p) and c(p). The perfectness of sequence spaces [ℓ...