alka munjal - Academia.edu (original) (raw)

Papers by alka munjal

The Nepali Mathematical Sciences Report

In the present study, a wider class of sequence is used for a least set of sufficient conditions ... more In the present study, a wider class of sequence is used for a least set of sufficient conditions for absolute Cesàro ϕ − |C, α, β; δ; γ| k summable factor for an infinite series. Many corollaries have been determined by using sutaible conditions in the main theorem. Validation of the theorem done by the previous findings of summablity. In this way, system's stability is improved by finding the conditions for absolute summability.

Systems Reliability Engineering, 2021

Soft Computing Techniques and Applications in Mechanical Engineering, 2018

Summability methods are a useful tool in dealing with the problems in the soft computing like in ... more Summability methods are a useful tool in dealing with the problems in the soft computing like in filtering of the signals and for stabilizing the systems. Signals can be in the form of various types of series (Infinite Series, Fourier series, etc.) and hence, summability theory is applicable in finding the error of approximation and degree of approximation of such signals. In this chapter, the authors gave an introductory discussion on summability theory and approximation of the signals. Further, they explained about the stability of the frequency response of the system. Also, they used the Fourier approximation in the soft computing models (multilayer perceptrons; radial basis function (RBF) or regularization networks, and fuzzy logic models) and found the output data of requirement.

Journal of Nepal Mathematical Society, 2020

In this study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two the... more In this study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ank ; δ) & (Ank ; γ; δ): Generalized summability method │A; δ │k & │A; γ; δ│k have been applied for determining the sufficient conditions, where k ≥ 1; δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.

International Journal of Analysis and Applications, 2017

A positive non-decreasing sequence has been used to establish a theorem on a minimal set of suffi... more A positive non-decreasing sequence has been used to establish a theorem on a minimal set of sufficient conditions for an infinite series to be absolute Cesaro varphi−∣C,1;delta;l∣k\varphi-|C, 1; \delta; l|_kvarphi−∣C,1;delta;l∣k summable. For some well-known applications, suitable conditions have been applied on the presented theorem for obtaining the sub-result of the presented theorem.

The Nepali Mathematical Sciences Report, 2020

In this paper, we determine that every n-tupled generalized Cesàro matrices (C, α1, α2, ..., αn; ... more In this paper, we determine that every n-tupled generalized Cesàro matrices (C, α1, α2, ..., αn; δ) ∈ B(A n k ; δ) for k ≥ 1, δ ≥ 0 and α1, α2, ..., αn > −1, need not be absolute k th power conservative since the Cesàro matrices of order α for α > −1 are not conservative matrices, where for some given k ≥ 1 and δ ≥ 0, if T ∈ B(A k , δ); i.e., if s0, s1, ...sn satisfying (0.1) ∞ n=1 n δk+k−1 |sn − sn−1| k < ∞, implies ∞ n=1 n δk+k−1 |tn − tn−1| k < ∞. Then, T is said to be absolutely k th power conservative.

The Nepali Mathematical Sciences Report, 2020

A result has been established for a conjugate trigonometric Fourier series in which degree of app... more A result has been established for a conjugate trigonometric Fourier series in which degree of approximation determine in class Lip (α, θ, w) by a product (C, 1)(E, q) mean (sequence to sequence transformation). This result is more applicable by using the product mean as it is used as double filter.

IOP Conference Series: Materials Science and Engineering, 2018

In the present study, two theorems explaining the degree of approximation of signals belonging to... more In the present study, two theorems explaining the degree of approximation of signals belonging to the class Lip(α, p, w) by a more general-method (Summability method) have been formulated. Improved estimations have been observed in terms of (); where (()) − ≤ − for 0 < ≤ 1 as compared to previous studies presented in terms of n. These estimations of infinite matrices are very much applicable in solid state physics which further motivates for an investigation of perturbations of matrix valued functions.

Publications de l'Institut Math?matique (Belgrade), 2019

We introduce |C,1|k summability for improper integrals and develop a generalized theorem based on... more We introduce |C,1|k summability for improper integrals and develop a generalized theorem based on absolute Ces?ro summability factor of an improper integral under sufficient conditions. We also derive some auxiliary results from the main ones.

International Journal of Mathematical, Engineering and Management Sciences, 2019

Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a m... more Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a minimal set of sufficient conditions for absolute Cesàro φ-|〖C,α;δ;l|〗_k summable factor. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. The presented main result has been validated by the previous result under suitable conditions. In this way, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved by finding a minimal set of sufficient conditions for absolute summability because absolute summable is the necessary and sufficient condition for BIBO stability.

International Journal of Engineering and Technology, 2017

In this paper, we defined the summability for integrals and established a theorem on absolute Nör... more In this paper, we defined the summability for integrals and established a theorem on absolute Nörlund summability |N, p n | k factors of improper integral under sufficient conditions. Some auxiliary results (well-known) have also been deduced from the main results under suitable conditions.

International Journal of Mathematical Analysis, 2016

In this paper, we established a generalized theorem on absolute summability factors by applying a... more In this paper, we established a generalized theorem on absolute summability factors by applying a recently defined absolute Cesàro summability ϕ − |C, 1; δ| k and the concept of a quasi-f-power increasing sequence for infinite series. We further obtained a well-known result under suitable conditions.

In this study, new sequence spaces (Ak, δ) & (Ak, γ; δ) have been introduced to establish two the... more In this study, new sequence spaces (Ak, δ) & (Ak, γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ak , δ) & (Ak , γ; δ). Generalized summability method |A, δ|k & |A, γ; δ|k have been applied for determining the sufficient conditions, where k ≥ 1, δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.

Journal of Inequalities and Applications, 2017

In this paper, we established a generalized theorem on a minimal set of sufficient conditions for... more In this paper, we established a generalized theorem on a minimal set of sufficient conditions for absolute summability factors by applying a sequence of a wider class (quasi-power increasing sequence) and the absolute Cesàro ϕ-|C, α, β; δ| k summability for an infinite series. We further obtained well-known applications of the above theorem as corollaries, under suitable conditions.

Procedia Computer Science, 2018

A theorem has been developed to acquire a set of conditions which is sufficient for an infinite s... more A theorem has been developed to acquire a set of conditions which is sufficient for an infinite series to be a generalized Cesàro φ-|C, α; δ| k summable using a wider class of sequence. Further, a conventional result has also been deduced from the main results under suitable conditions, which is a validation of the present result by the previous result. Using quasi 'f ' power increasing sequence, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved for modelling an infinite series to be absolute summable by estimating sufficient conditions which are also necessary and sufficient conditions for an infinite series to be BIBO stable.

The Nepali Mathematical Sciences Report

In the present study, a wider class of sequence is used for a least set of sufficient conditions ... more In the present study, a wider class of sequence is used for a least set of sufficient conditions for absolute Cesàro ϕ − |C, α, β; δ; γ| k summable factor for an infinite series. Many corollaries have been determined by using sutaible conditions in the main theorem. Validation of the theorem done by the previous findings of summablity. In this way, system's stability is improved by finding the conditions for absolute summability.

Systems Reliability Engineering, 2021

Soft Computing Techniques and Applications in Mechanical Engineering, 2018

Summability methods are a useful tool in dealing with the problems in the soft computing like in ... more Summability methods are a useful tool in dealing with the problems in the soft computing like in filtering of the signals and for stabilizing the systems. Signals can be in the form of various types of series (Infinite Series, Fourier series, etc.) and hence, summability theory is applicable in finding the error of approximation and degree of approximation of such signals. In this chapter, the authors gave an introductory discussion on summability theory and approximation of the signals. Further, they explained about the stability of the frequency response of the system. Also, they used the Fourier approximation in the soft computing models (multilayer perceptrons; radial basis function (RBF) or regularization networks, and fuzzy logic models) and found the output data of requirement.

Journal of Nepal Mathematical Society, 2020

In this study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two the... more In this study, new sequence spaces (Ak; δ) & (Ak; γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ank ; δ) & (Ank ; γ; δ): Generalized summability method │A; δ │k & │A; γ; δ│k have been applied for determining the sufficient conditions, where k ≥ 1; δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.

International Journal of Analysis and Applications, 2017

A positive non-decreasing sequence has been used to establish a theorem on a minimal set of suffi... more A positive non-decreasing sequence has been used to establish a theorem on a minimal set of sufficient conditions for an infinite series to be absolute Cesaro varphi−∣C,1;delta;l∣k\varphi-|C, 1; \delta; l|_kvarphi−∣C,1;delta;l∣k summable. For some well-known applications, suitable conditions have been applied on the presented theorem for obtaining the sub-result of the presented theorem.

The Nepali Mathematical Sciences Report, 2020

In this paper, we determine that every n-tupled generalized Cesàro matrices (C, α1, α2, ..., αn; ... more In this paper, we determine that every n-tupled generalized Cesàro matrices (C, α1, α2, ..., αn; δ) ∈ B(A n k ; δ) for k ≥ 1, δ ≥ 0 and α1, α2, ..., αn > −1, need not be absolute k th power conservative since the Cesàro matrices of order α for α > −1 are not conservative matrices, where for some given k ≥ 1 and δ ≥ 0, if T ∈ B(A k , δ); i.e., if s0, s1, ...sn satisfying (0.1) ∞ n=1 n δk+k−1 |sn − sn−1| k < ∞, implies ∞ n=1 n δk+k−1 |tn − tn−1| k < ∞. Then, T is said to be absolutely k th power conservative.

The Nepali Mathematical Sciences Report, 2020

A result has been established for a conjugate trigonometric Fourier series in which degree of app... more A result has been established for a conjugate trigonometric Fourier series in which degree of approximation determine in class Lip (α, θ, w) by a product (C, 1)(E, q) mean (sequence to sequence transformation). This result is more applicable by using the product mean as it is used as double filter.

IOP Conference Series: Materials Science and Engineering, 2018

In the present study, two theorems explaining the degree of approximation of signals belonging to... more In the present study, two theorems explaining the degree of approximation of signals belonging to the class Lip(α, p, w) by a more general-method (Summability method) have been formulated. Improved estimations have been observed in terms of (); where (()) − ≤ − for 0 < ≤ 1 as compared to previous studies presented in terms of n. These estimations of infinite matrices are very much applicable in solid state physics which further motivates for an investigation of perturbations of matrix valued functions.

Publications de l'Institut Math?matique (Belgrade), 2019

We introduce |C,1|k summability for improper integrals and develop a generalized theorem based on... more We introduce |C,1|k summability for improper integrals and develop a generalized theorem based on absolute Ces?ro summability factor of an improper integral under sufficient conditions. We also derive some auxiliary results from the main ones.

International Journal of Mathematical, Engineering and Management Sciences, 2019

Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a m... more Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a minimal set of sufficient conditions for absolute Cesàro φ-|〖C,α;δ;l|〗_k summable factor. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. The presented main result has been validated by the previous result under suitable conditions. In this way, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved by finding a minimal set of sufficient conditions for absolute summability because absolute summable is the necessary and sufficient condition for BIBO stability.

International Journal of Engineering and Technology, 2017

In this paper, we defined the summability for integrals and established a theorem on absolute Nör... more In this paper, we defined the summability for integrals and established a theorem on absolute Nörlund summability |N, p n | k factors of improper integral under sufficient conditions. Some auxiliary results (well-known) have also been deduced from the main results under suitable conditions.

International Journal of Mathematical Analysis, 2016

In this paper, we established a generalized theorem on absolute summability factors by applying a... more In this paper, we established a generalized theorem on absolute summability factors by applying a recently defined absolute Cesàro summability ϕ − |C, 1; δ| k and the concept of a quasi-f-power increasing sequence for infinite series. We further obtained a well-known result under suitable conditions.

In this study, new sequence spaces (Ak, δ) & (Ak, γ; δ) have been introduced to establish two the... more In this study, new sequence spaces (Ak, δ) & (Ak, γ; δ) have been introduced to establish two theorems on minimal set of the sufficient conditions for a n-tupled triangle T to be a bounded operator on sequence spaces (Ak , δ) & (Ak , γ; δ). Generalized summability method |A, δ|k & |A, γ; δ|k have been applied for determining the sufficient conditions, where k ≥ 1, δ ≥ 0 and γ is real number. Further, a set of new and well-known applications has been deduced from the main result under suitable conditions, which shows the importance of the main result.

Journal of Inequalities and Applications, 2017

In this paper, we established a generalized theorem on a minimal set of sufficient conditions for... more In this paper, we established a generalized theorem on a minimal set of sufficient conditions for absolute summability factors by applying a sequence of a wider class (quasi-power increasing sequence) and the absolute Cesàro ϕ-|C, α, β; δ| k summability for an infinite series. We further obtained well-known applications of the above theorem as corollaries, under suitable conditions.

Procedia Computer Science, 2018

A theorem has been developed to acquire a set of conditions which is sufficient for an infinite s... more A theorem has been developed to acquire a set of conditions which is sufficient for an infinite series to be a generalized Cesàro φ-|C, α; δ| k summable using a wider class of sequence. Further, a conventional result has also been deduced from the main results under suitable conditions, which is a validation of the present result by the previous result. Using quasi 'f ' power increasing sequence, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved for modelling an infinite series to be absolute summable by estimating sufficient conditions which are also necessary and sufficient conditions for an infinite series to be BIBO stable.