Journal of Nepal Mathematical Society, Aug 21, 2023
The hypergeometric series is an extension of the geometric series. The confluent hypergeometric f... more The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ + b -1) -z(θ + a)]w = 0. Kummer's first formula and Kummer's second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w 1 (z), w 2 (z), w 3 (z), w 4 (z), w 5 (z) and w 6 (z) as the combination of three solutions.
Journal of Nepal Mathematical Society, Feb 26, 2024
The aim of this paper is to introduce and study a new class ℓ 2 ((X, ||.||),γ,ω) of double sequen... more The aim of this paper is to introduce and study a new class ℓ 2 ((X, ||.||),γ,ω) of double sequences with their terms in a normed space X as a generalization of the familiar sequence space ℓ. Besides the investigation of the condition pertaining to the containment relations of the class ℓ 2 ((X, ||.||),γ,ω) of same kind in terms ofγ andω, our primary interest is to explore some of the preliminary results that characterize the linear topological structures of ℓ 2 ((X, ||.||),γ,ω) when topologized it with suitable natural paranorm.
In this research note, we have obtained some new classical summation relations of certain Appell'... more In this research note, we have obtained some new classical summation relations of certain Appell's double hypergeometric functions associated with theory of approximation. This novel relation include, as special case, a set of well-known results. It studies the famous works of the authors [1], [2], [14], [15], [33] -[38].
Journal of Nepal Mathematical Society, Aug 21, 2023
The hypergeometric series is an extension of the geometric series. The confluent hypergeometric f... more The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ + b − 1) − z(θ + a)]w = 0. Kummer's first formula and Kummer's second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w 1 (z), w 2 (z), w 3 (z), w 4 (z), w 5 (z) and w 6 (z) as the combination of three solutions.
The hypergeometric functions are one of the most important and special functions in mathematics. ... more The hypergeometric functions are one of the most important and special functions in mathematics. They are the generalization of the exponential functions. Particularly the ordinary hypergeometric function 2F1(a, b; c; z) is represented by hypergeometric series and is a solution to a second order differential equation. Similarly, Laplace transform is a form of integral transform that converts linear differential equations to algebraic equations. This paper aims to study the convergence of hypergeometric function and Laplace transform of some hypergeometric functions. Moreover, some relationships between Laplace transformation and hypergeometric functions is established in the concluding section of this paper.
In this research note, we have obtained some new classical summation relations of certain Appell'... more In this research note, we have obtained some new classical summation relations of certain Appell's double hypergeometric functions associated with theory of approximation. This novel relation include, as special case, a set of well-known results. It studies the famous works of the authors [1], [2], [14], [15], [33]-[38].
International journal of statistics and applied mathematics, Jul 1, 2023
The eastern society is rich in terms of science and technology. Mathematics is considered as the ... more The eastern society is rich in terms of science and technology. Mathematics is considered as the base of science. The eastern history shows that the Hindu society is rich in mathematics. The evolution of mathematics can be studied from the time of 'patiganita' to the latest form of science and technology. Geometric series is an important tool in arithmetic which is now developed to hypergeometric function. Hypergeometric function is an advance function used to solve differential equations of second order. The purpose of this paper is to find the linkage between the ancient geometric series (Gunanka sreni) to the modern Hypergeometric function and to expose the work of ancient Hindu mathematicians which is believed to be narrow among the mathematics researchers of the present period. In this paper, some forms of geometric series that were used in Hindu mathematics are interpreted in terms of hypergeometric series.
Shrinking atomic decompositions in locally convex Banach spaces were studied by Carando and Lassa... more Shrinking atomic decompositions in locally convex Banach spaces were studied by Carando and Lassalle [2]. In this paper, we define strongly shrinking atomic decompositions in p-Banach spaces and give necessary and sufficient condition for atomic decomposition to be shrinking and boundedly complete.
The hypergeometric functions are one of the most important and special functions in mathematics. ... more The hypergeometric functions are one of the most important and special functions in mathematics. They are the generalization of the exponential functions. Particularly the ordinary hypergeometric function 2F1(a, b; c; z) is represented by hypergeometric series and is a solution to a second order differential equation. Similarly, Laplace transform is a form of integral transform that converts linear differential equations to algebraic equations. This paper aims to study the convergence of hypergeometric function and Laplace transform of some hypergeometric functions. Moreover, some relationships between Laplace transformation and hypergeometric functions is established in the concluding section of this paper.
In the present work, we introduce the difference sequence spaces W I 0 (||. ,. ||, M, , a, ), W... more In the present work, we introduce the difference sequence spaces W I 0 (||. ,. ||, M, , a, ), W I (||. ,. ||, M, , a, ) and W I (||. ,. ||, M, , a, ) in 2-normed space using Orlicz function and ideal convergence. We will examine some of their topological properties.
Lotfi A. Zadeh developed the concept of fuzzy logic in 1965, and it has since been applied to the... more Lotfi A. Zadeh developed the concept of fuzzy logic in 1965, and it has since been applied to the study of various class spaces. This research aims to investigate the linearity and some topological properties of the generalized form of difference sequence spaces � (
The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of re... more The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of research in social science, management science, and mathematics. In this paper, we use the concept of Fuzzy real numbers to introduce and study the new double sequence spaces l∞ (M, λ, ρ), C F (M, λ, ρ) and CoF (M, λ, ρ) of fuzzy real numbers defined by the Orlicz function and study some of their properties like linear space structure, completeness, and solidness.
In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ... more In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ||.||) valued difference sequences with the help of Orlicz function M . This is a generalization of the classical sequence space c0. Our primary interest is to explore some linear structures and investigate the conditions relating to the containment relation of the class c0 (M, (X, ||.||), ā, ᾱ) in terms of different ā and ᾱ.
So far a large number of research works have been studied and investigated in basic sequence spac... more So far a large number of research works have been studied and investigated in basic sequence spaces c0, c, and l∞. In this present work, we introduce the difference sequence spaces W0(∆, f), W(∆, f) and W∞(∆, f) defined by non-negative real-valued Φ- function on R and study some of their topological properties defined by the paranormed structure on these spaces.
Fuzzy Logic is a multiple valued logic, from which the truth values of variables might be any rea... more Fuzzy Logic is a multiple valued logic, from which the truth values of variables might be any real numbers between 0 and 1. It has wide application in different fields of real life. We might face different challenges in our daily life to select the best of the best for the concrete result. There are various criteria in the literature for ranking alternatives in the realm of decision-making under uncertainty in a crisp environment. In this paper, we address the challenges seen in making a decision for selecting the best of the best as studied by Bellmen-Zadeh maximin method. It is used to address such challenges using fuzzy real numbers.
Fuzzy metric spaces theory is important in mathematics, statistics, computer science, and other f... more Fuzzy metric spaces theory is important in mathematics, statistics, computer science, and other fields. In this paper fundamental characteristics of the fuzzy metric space are examined. The notions of fuzzy convergent sequence, fuzzy Cauchy sequence, fuzzy open ball, are reviewed with theorems associated with these concepts.
The aim of this paper is to introduce and study a new class c 0 (( S , ||. , .||), F , ) ... more The aim of this paper is to introduce and study a new class c 0 (( S , ||. , .||), F , ) of 2-normed space valued vector sequences using Orlicz function as a generalization of the basic space c 0 of all converging sequences. Beside the investigation pertaining to the linear space structures of the class c 0 (( S , ||. , .||), F , ) with some topological properties, our primarily interest is to explore the containment relation of the class c 0 (( S , ||. , .||), F , ) in terms of different values of . Keywords: Sequence space, Normal Space , 2- normed Space, Orlicz Function, Orlicz Space. 2010 AMS Subject Classification : Primary - 46A45 , Secondary - 46B 15
In this paper, we prove a main theorem dealing the matrix summability of Legendre series using no... more In this paper, we prove a main theorem dealing the matrix summability of Legendre series using non-negative monotonic non-increasing sequences of function. This paper is more general than [9], [12] and [22].
The aim of this paper is to introduce and study a new class (l ∞ (X, Y, Φ, ξ, w , L), H U ) of lo... more The aim of this paper is to introduce and study a new class (l ∞ (X, Y, Φ, ξ, w , L), H U ) of locally convex space Y- valued functions using Orlicz function Φ as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the linear topological structures of the class (l ∞ (X, Y, Φ, ξ, w , L), H U ) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class l ∞ (X, Y, Φ , ξ, w) in terms of different ξ and w so that such a class of functions is contained in or equal to another class of similar nature.
Journal of Nepal Mathematical Society, Aug 21, 2023
The hypergeometric series is an extension of the geometric series. The confluent hypergeometric f... more The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ + b -1) -z(θ + a)]w = 0. Kummer's first formula and Kummer's second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w 1 (z), w 2 (z), w 3 (z), w 4 (z), w 5 (z) and w 6 (z) as the combination of three solutions.
Journal of Nepal Mathematical Society, Feb 26, 2024
The aim of this paper is to introduce and study a new class ℓ 2 ((X, ||.||),γ,ω) of double sequen... more The aim of this paper is to introduce and study a new class ℓ 2 ((X, ||.||),γ,ω) of double sequences with their terms in a normed space X as a generalization of the familiar sequence space ℓ. Besides the investigation of the condition pertaining to the containment relations of the class ℓ 2 ((X, ||.||),γ,ω) of same kind in terms ofγ andω, our primary interest is to explore some of the preliminary results that characterize the linear topological structures of ℓ 2 ((X, ||.||),γ,ω) when topologized it with suitable natural paranorm.
In this research note, we have obtained some new classical summation relations of certain Appell'... more In this research note, we have obtained some new classical summation relations of certain Appell's double hypergeometric functions associated with theory of approximation. This novel relation include, as special case, a set of well-known results. It studies the famous works of the authors [1], [2], [14], [15], [33] -[38].
Journal of Nepal Mathematical Society, Aug 21, 2023
The hypergeometric series is an extension of the geometric series. The confluent hypergeometric f... more The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ + b − 1) − z(θ + a)]w = 0. Kummer's first formula and Kummer's second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w 1 (z), w 2 (z), w 3 (z), w 4 (z), w 5 (z) and w 6 (z) as the combination of three solutions.
The hypergeometric functions are one of the most important and special functions in mathematics. ... more The hypergeometric functions are one of the most important and special functions in mathematics. They are the generalization of the exponential functions. Particularly the ordinary hypergeometric function 2F1(a, b; c; z) is represented by hypergeometric series and is a solution to a second order differential equation. Similarly, Laplace transform is a form of integral transform that converts linear differential equations to algebraic equations. This paper aims to study the convergence of hypergeometric function and Laplace transform of some hypergeometric functions. Moreover, some relationships between Laplace transformation and hypergeometric functions is established in the concluding section of this paper.
In this research note, we have obtained some new classical summation relations of certain Appell'... more In this research note, we have obtained some new classical summation relations of certain Appell's double hypergeometric functions associated with theory of approximation. This novel relation include, as special case, a set of well-known results. It studies the famous works of the authors [1], [2], [14], [15], [33]-[38].
International journal of statistics and applied mathematics, Jul 1, 2023
The eastern society is rich in terms of science and technology. Mathematics is considered as the ... more The eastern society is rich in terms of science and technology. Mathematics is considered as the base of science. The eastern history shows that the Hindu society is rich in mathematics. The evolution of mathematics can be studied from the time of 'patiganita' to the latest form of science and technology. Geometric series is an important tool in arithmetic which is now developed to hypergeometric function. Hypergeometric function is an advance function used to solve differential equations of second order. The purpose of this paper is to find the linkage between the ancient geometric series (Gunanka sreni) to the modern Hypergeometric function and to expose the work of ancient Hindu mathematicians which is believed to be narrow among the mathematics researchers of the present period. In this paper, some forms of geometric series that were used in Hindu mathematics are interpreted in terms of hypergeometric series.
Shrinking atomic decompositions in locally convex Banach spaces were studied by Carando and Lassa... more Shrinking atomic decompositions in locally convex Banach spaces were studied by Carando and Lassalle [2]. In this paper, we define strongly shrinking atomic decompositions in p-Banach spaces and give necessary and sufficient condition for atomic decomposition to be shrinking and boundedly complete.
The hypergeometric functions are one of the most important and special functions in mathematics. ... more The hypergeometric functions are one of the most important and special functions in mathematics. They are the generalization of the exponential functions. Particularly the ordinary hypergeometric function 2F1(a, b; c; z) is represented by hypergeometric series and is a solution to a second order differential equation. Similarly, Laplace transform is a form of integral transform that converts linear differential equations to algebraic equations. This paper aims to study the convergence of hypergeometric function and Laplace transform of some hypergeometric functions. Moreover, some relationships between Laplace transformation and hypergeometric functions is established in the concluding section of this paper.
In the present work, we introduce the difference sequence spaces W I 0 (||. ,. ||, M, , a, ), W... more In the present work, we introduce the difference sequence spaces W I 0 (||. ,. ||, M, , a, ), W I (||. ,. ||, M, , a, ) and W I (||. ,. ||, M, , a, ) in 2-normed space using Orlicz function and ideal convergence. We will examine some of their topological properties.
Lotfi A. Zadeh developed the concept of fuzzy logic in 1965, and it has since been applied to the... more Lotfi A. Zadeh developed the concept of fuzzy logic in 1965, and it has since been applied to the study of various class spaces. This research aims to investigate the linearity and some topological properties of the generalized form of difference sequence spaces � (
The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of re... more The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of research in social science, management science, and mathematics. In this paper, we use the concept of Fuzzy real numbers to introduce and study the new double sequence spaces l∞ (M, λ, ρ), C F (M, λ, ρ) and CoF (M, λ, ρ) of fuzzy real numbers defined by the Orlicz function and study some of their properties like linear space structure, completeness, and solidness.
In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ... more In this article, we introduce and study a new class c0 (M, (X, ||.||), ā, ᾱ) of normed space (X, ||.||) valued difference sequences with the help of Orlicz function M . This is a generalization of the classical sequence space c0. Our primary interest is to explore some linear structures and investigate the conditions relating to the containment relation of the class c0 (M, (X, ||.||), ā, ᾱ) in terms of different ā and ᾱ.
So far a large number of research works have been studied and investigated in basic sequence spac... more So far a large number of research works have been studied and investigated in basic sequence spaces c0, c, and l∞. In this present work, we introduce the difference sequence spaces W0(∆, f), W(∆, f) and W∞(∆, f) defined by non-negative real-valued Φ- function on R and study some of their topological properties defined by the paranormed structure on these spaces.
Fuzzy Logic is a multiple valued logic, from which the truth values of variables might be any rea... more Fuzzy Logic is a multiple valued logic, from which the truth values of variables might be any real numbers between 0 and 1. It has wide application in different fields of real life. We might face different challenges in our daily life to select the best of the best for the concrete result. There are various criteria in the literature for ranking alternatives in the realm of decision-making under uncertainty in a crisp environment. In this paper, we address the challenges seen in making a decision for selecting the best of the best as studied by Bellmen-Zadeh maximin method. It is used to address such challenges using fuzzy real numbers.
Fuzzy metric spaces theory is important in mathematics, statistics, computer science, and other f... more Fuzzy metric spaces theory is important in mathematics, statistics, computer science, and other fields. In this paper fundamental characteristics of the fuzzy metric space are examined. The notions of fuzzy convergent sequence, fuzzy Cauchy sequence, fuzzy open ball, are reviewed with theorems associated with these concepts.
The aim of this paper is to introduce and study a new class c 0 (( S , ||. , .||), F , ) ... more The aim of this paper is to introduce and study a new class c 0 (( S , ||. , .||), F , ) of 2-normed space valued vector sequences using Orlicz function as a generalization of the basic space c 0 of all converging sequences. Beside the investigation pertaining to the linear space structures of the class c 0 (( S , ||. , .||), F , ) with some topological properties, our primarily interest is to explore the containment relation of the class c 0 (( S , ||. , .||), F , ) in terms of different values of . Keywords: Sequence space, Normal Space , 2- normed Space, Orlicz Function, Orlicz Space. 2010 AMS Subject Classification : Primary - 46A45 , Secondary - 46B 15
In this paper, we prove a main theorem dealing the matrix summability of Legendre series using no... more In this paper, we prove a main theorem dealing the matrix summability of Legendre series using non-negative monotonic non-increasing sequences of function. This paper is more general than [9], [12] and [22].
The aim of this paper is to introduce and study a new class (l ∞ (X, Y, Φ, ξ, w , L), H U ) of lo... more The aim of this paper is to introduce and study a new class (l ∞ (X, Y, Φ, ξ, w , L), H U ) of locally convex space Y- valued functions using Orlicz function Φ as a generalization of some of the well known sequence spaces and function spaces. Besides the investigation pertaining to the linear topological structures of the class (l ∞ (X, Y, Φ, ξ, w , L), H U ) when topologized it with suitable natural paranorm , our primarily interest is to explore the conditions pertaining the containment relation of the class l ∞ (X, Y, Φ , ξ, w) in terms of different ξ and w so that such a class of functions is contained in or equal to another class of similar nature.
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