Revista y Edición

Volumen 29 (2021): Edición 2 (December 2021)

Volumen 29 (2021): Edición 1 (June 2021)

Volumen 28 (2020): Edición 2 (December 2020)

Volumen 28 (2020): Edición 1 (June 2020)

Volumen 27 (2019): Edición 2 (December 2019)

Volumen 27 (2019): Edición 1 (June 2019)

Detalles de la revista
Formato
Revista
eISSN
1584-3289
Publicado por primera vez
30 Jul 2019
Periodo de publicación
2 veces al año
Idiomas
Inglés

Buscar

Volumen 28 (2020): Edición 1 (June 2020)

Detalles de la revista
Formato
Revista
eISSN
1584-3289
Publicado por primera vez
30 Jul 2019
Periodo de publicación
2 veces al año
Idiomas
Inglés

Buscar

10 Artículos
Acceso abierto

On graded derivations of superalgebras

Publicado en línea: 31 Jul 2020
Páginas: 3 - 10

Resumen

Abstract

In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (g, [, ]) is skew-supersymmetry and satisfies the super Jacobi identity, so it defines the structure of a Lie superalgebra on g.

In the case of the algebra of differential forms on a supermanifold, we study the graded commutator of graded derivations, graded skew-derivations and a graded derivation, with another graded skew-derivation of the superalgebra of differential forms on a supermanifold.

Palabras clave

  • graded manifolds
  • Lie superalgebra
  • graded derivation
  • graded skew-derivation

MSC 2010

  • 13N15
  • 17B70
  • 58A50
Acceso abierto

Uniqueness of p(f) and P [f] concerning weakly weighted-sharing

Publicado en línea: 31 Jul 2020
Páginas: 11 - 24

Resumen

Abstract

In the year 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between “CM” and “IM”. In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of a polynomial function p(f) of f and a homogeneous differential polynomial P [f] generated by f. Our results improve and generalizes the results due to Charak and Lal, S. Lin and W. Lin, and H-Y Xu and Y Hu.

Palabras clave

  • Meromorphic function
  • Weakly weighted share
  • Small function
  • Differential polynomial

MSC 2010

  • 3030
  • 3035
Acceso abierto

Some Hadamard and Simpson type inequalities via s-convexity and their applications

Publicado en línea: 31 Jul 2020
Páginas: 25 - 39

Resumen

Abstract

In this study, the authors establish and generalize some inequalities of Hadamard and Simpson type based on s-convexity in the second sense. Some applications are also given and generalized. Examples are given to show the results. The results generalize the integral inequalities in articles of Sarikaya and Xi.

Palabras clave

  • -convex functions
  • Hadamard inequality
  • Simpson inequality
  • Bullen inequality

MSC 2010

  • 26D07
  • 26D15
Acceso abierto

Common fixed points under contractive conditions of integral type

Publicado en línea: 31 Jul 2020
Páginas: 41 - 57

Resumen

Abstract

In this paper, we give some common fixed point theorems for a class of occasionally weakly compatible mappings satisfying contractive conditions of integral type. Our results generalize a host of previously theorems. We also present some illustrative examples which support our main results and show the applicability and validity of these results.

Palabras clave

  • Weakly compatible mappings
  • occasionally weakly compatible mappings
  • contractive conditions
  • integral type
  • common fixed point theorems

MSC 2010

  • 47H10
  • 54H25
Acceso abierto

Calculus for the intermediate point associated with a mean value theorem of the integral calculus

Publicado en línea: 31 Jul 2020
Páginas: 59 - 66

Resumen

Abstract

If f, g: [a, b] → 𝕉 are two continuous functions, then there exists a point c ∈ (a, b) such that

acf(x)dx+(c-a)g(c)=cbg(x)dx+(b-c)f(c).\int_a^c {f\left(x \right)} dx + \left({c - a} \right)g\left(c \right) = \int_c^b {g\left(x \right)} dx + \left({b - c} \right)f\left(c \right).

In this paper, we study the approaching of the point c towards a, when b approaches a.

Palabras clave

  • intermediate point
  • mean-value theorem

MSC 2010

  • 26A24
  • 11H60
Acceso abierto

A refinement of Grüss inequality for the complex integral

Publicado en línea: 31 Jul 2020
Páginas: 67 - 83

Resumen

Abstract

Assume that f and g are continuous on γ, γ ⊂ 𝔺 is a piecewise smooth path parametrized by z (t), t ∈ [a, b] from z (a) = u to z (b) = w with wu and the complex Čebyšev functional is defined by

𝒟γ(f,g):=1w-uγf(z)g(z)dz-1w-uγf(z)dz1w-uγg(z)dz.{{\cal D}_\gamma}\left({f,g} \right): = {1 \over {w - u}}\int_\gamma {f\left(z \right)} g\left(z \right)dz - {1 \over {w - u}}\int_\gamma {f\left(z \right)} dz{1 \over {w - u}}\int_\gamma {g\left(z \right)} dz.

In this paper we establish some Grüss type inequalities for 𝒟 (f, g) under some complex boundedness conditions for the functions f and g.

Palabras clave

  • Complex integral
  • Continuous functions
  • Holomorphic functions
  • Grüss inequality

MSC 2010

  • 26D15
  • 26D10
  • 30A10
  • 30A86
Acceso abierto

Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients II

Publicado en línea: 31 Jul 2020
Páginas: 85 - 103

Resumen

Abstract

In this paper, we study a class of univalent functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying

Re{z(J1λ,μf(z))'(1-γ)J1λ,μf(z)+γz2(J1λ,μf(z))''}>β.{\mathop{\rm Re}\nolimits} \left\{{{{z\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)'} \over {\left({1 - \gamma} \right){\bf{J}}_1^{\lambda,\mu}f\left(z \right) + \gamma {z^2}\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)''}}} \right\} > \beta.

A necessary and sufficient condition for a function to be in the class Aγλ,μ,ν(n,β)A_\gamma ^{\lambda,\mu,\nu}\left({n,\beta} \right) is obtained. Also, our paper includes linear combination, integral operators and we introduce the subclass Aγ,cmλ,μ,ν(1,β)A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right) consisting of functions with negative and fixed finitely many coefficients. We study some interesting properties of Aγ,cmλ,μ,ν(1,β)A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right).

Palabras clave

  • Generalized Ruscheweyh derivatives
  • Fractional derivative
  • Integral operators
  • Linear combination
  • Radii of starlikeness
  • Extreme points
  • Weighted mean and Arithmetic mean

MSC 2010

  • 30C45
  • 30C50
Acceso abierto

Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

Publicado en línea: 31 Jul 2020
Páginas: 105 - 114

Resumen

Abstract

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

Palabras clave

  • Differential operator
  • univalent function
  • analytic function
  • subordination
  • unit disk
  • inequality

MSC 2010

  • 30C45
  • 30C55
Acceso abierto

A differential inequality involving Ruscheweyh operator and univalent functions

Publicado en línea: 31 Jul 2020
Páginas: 115 - 123

Resumen

Abstract

In the present paper, we find certain results on Ruscheweyh operator using differential inequality. In particular, we find sufficient conditions for starlike and convex functions.

Palabras clave

  • Analytic function
  • convex function
  • starlike function
  • Ruscheweyh operator

MSC 2010

  • 30C45
Acceso abierto

Certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers

Publicado en línea: 31 Jul 2020
Páginas: 125 - 140

Resumen

Abstract

This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients |a2| and |a3| for the functions in these classes. Also we investigate upper bounds for the Fekete-Szegö functional and second Hankel determinant for these classes.

Palabras clave

  • Sãlãgean operator
  • bi-univalent functions
  • subordination
  • shell-like curves
  • univalent functions
  • starlike functions
  • convex functions
  • Fibonacci numbers

MSC 2010

  • 30C45
  • 30C50
10 Artículos
Acceso abierto

On graded derivations of superalgebras

Publicado en línea: 31 Jul 2020
Páginas: 3 - 10

Resumen

Abstract

In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (g, [, ]) is skew-supersymmetry and satisfies the super Jacobi identity, so it defines the structure of a Lie superalgebra on g.

In the case of the algebra of differential forms on a supermanifold, we study the graded commutator of graded derivations, graded skew-derivations and a graded derivation, with another graded skew-derivation of the superalgebra of differential forms on a supermanifold.

Palabras clave

  • graded manifolds
  • Lie superalgebra
  • graded derivation
  • graded skew-derivation

MSC 2010

  • 13N15
  • 17B70
  • 58A50
Acceso abierto

Uniqueness of p(f) and P [f] concerning weakly weighted-sharing

Publicado en línea: 31 Jul 2020
Páginas: 11 - 24

Resumen

Abstract

In the year 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between “CM” and “IM”. In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of a polynomial function p(f) of f and a homogeneous differential polynomial P [f] generated by f. Our results improve and generalizes the results due to Charak and Lal, S. Lin and W. Lin, and H-Y Xu and Y Hu.

Palabras clave

  • Meromorphic function
  • Weakly weighted share
  • Small function
  • Differential polynomial

MSC 2010

  • 3030
  • 3035
Acceso abierto

Some Hadamard and Simpson type inequalities via s-convexity and their applications

Publicado en línea: 31 Jul 2020
Páginas: 25 - 39

Resumen

Abstract

In this study, the authors establish and generalize some inequalities of Hadamard and Simpson type based on s-convexity in the second sense. Some applications are also given and generalized. Examples are given to show the results. The results generalize the integral inequalities in articles of Sarikaya and Xi.

Palabras clave

  • -convex functions
  • Hadamard inequality
  • Simpson inequality
  • Bullen inequality

MSC 2010

  • 26D07
  • 26D15
Acceso abierto

Common fixed points under contractive conditions of integral type

Publicado en línea: 31 Jul 2020
Páginas: 41 - 57

Resumen

Abstract

In this paper, we give some common fixed point theorems for a class of occasionally weakly compatible mappings satisfying contractive conditions of integral type. Our results generalize a host of previously theorems. We also present some illustrative examples which support our main results and show the applicability and validity of these results.

Palabras clave

  • Weakly compatible mappings
  • occasionally weakly compatible mappings
  • contractive conditions
  • integral type
  • common fixed point theorems

MSC 2010

  • 47H10
  • 54H25
Acceso abierto

Calculus for the intermediate point associated with a mean value theorem of the integral calculus

Publicado en línea: 31 Jul 2020
Páginas: 59 - 66

Resumen

Abstract

If f, g: [a, b] → 𝕉 are two continuous functions, then there exists a point c ∈ (a, b) such that

acf(x)dx+(c-a)g(c)=cbg(x)dx+(b-c)f(c).\int_a^c {f\left(x \right)} dx + \left({c - a} \right)g\left(c \right) = \int_c^b {g\left(x \right)} dx + \left({b - c} \right)f\left(c \right).

In this paper, we study the approaching of the point c towards a, when b approaches a.

Palabras clave

  • intermediate point
  • mean-value theorem

MSC 2010

  • 26A24
  • 11H60
Acceso abierto

A refinement of Grüss inequality for the complex integral

Publicado en línea: 31 Jul 2020
Páginas: 67 - 83

Resumen

Abstract

Assume that f and g are continuous on γ, γ ⊂ 𝔺 is a piecewise smooth path parametrized by z (t), t ∈ [a, b] from z (a) = u to z (b) = w with wu and the complex Čebyšev functional is defined by

𝒟γ(f,g):=1w-uγf(z)g(z)dz-1w-uγf(z)dz1w-uγg(z)dz.{{\cal D}_\gamma}\left({f,g} \right): = {1 \over {w - u}}\int_\gamma {f\left(z \right)} g\left(z \right)dz - {1 \over {w - u}}\int_\gamma {f\left(z \right)} dz{1 \over {w - u}}\int_\gamma {g\left(z \right)} dz.

In this paper we establish some Grüss type inequalities for 𝒟 (f, g) under some complex boundedness conditions for the functions f and g.

Palabras clave

  • Complex integral
  • Continuous functions
  • Holomorphic functions
  • Grüss inequality

MSC 2010

  • 26D15
  • 26D10
  • 30A10
  • 30A86
Acceso abierto

Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients II

Publicado en línea: 31 Jul 2020
Páginas: 85 - 103

Resumen

Abstract

In this paper, we study a class of univalent functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying

Re{z(J1λ,μf(z))'(1-γ)J1λ,μf(z)+γz2(J1λ,μf(z))''}>β.{\mathop{\rm Re}\nolimits} \left\{{{{z\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)'} \over {\left({1 - \gamma} \right){\bf{J}}_1^{\lambda,\mu}f\left(z \right) + \gamma {z^2}\left({{\bf{J}}_1^{\lambda,\mu}f\left(z \right)} \right)''}}} \right\} > \beta.

A necessary and sufficient condition for a function to be in the class Aγλ,μ,ν(n,β)A_\gamma ^{\lambda,\mu,\nu}\left({n,\beta} \right) is obtained. Also, our paper includes linear combination, integral operators and we introduce the subclass Aγ,cmλ,μ,ν(1,β)A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right) consisting of functions with negative and fixed finitely many coefficients. We study some interesting properties of Aγ,cmλ,μ,ν(1,β)A_{\gamma,{c_m}}^{\lambda,\mu,\nu}\left({1,\beta} \right).

Palabras clave

  • Generalized Ruscheweyh derivatives
  • Fractional derivative
  • Integral operators
  • Linear combination
  • Radii of starlikeness
  • Extreme points
  • Weighted mean and Arithmetic mean

MSC 2010

  • 30C45
  • 30C50
Acceso abierto

Generalized Briot-Bouquet differential equation based on new differential operator with complex connections

Publicado en línea: 31 Jul 2020
Páginas: 105 - 114

Resumen

Abstract

Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.

Palabras clave

  • Differential operator
  • univalent function
  • analytic function
  • subordination
  • unit disk
  • inequality

MSC 2010

  • 30C45
  • 30C55
Acceso abierto

A differential inequality involving Ruscheweyh operator and univalent functions

Publicado en línea: 31 Jul 2020
Páginas: 115 - 123

Resumen

Abstract

In the present paper, we find certain results on Ruscheweyh operator using differential inequality. In particular, we find sufficient conditions for starlike and convex functions.

Palabras clave

  • Analytic function
  • convex function
  • starlike function
  • Ruscheweyh operator

MSC 2010

  • 30C45
Acceso abierto

Certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers

Publicado en línea: 31 Jul 2020
Páginas: 125 - 140

Resumen

Abstract

This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients |a2| and |a3| for the functions in these classes. Also we investigate upper bounds for the Fekete-Szegö functional and second Hankel determinant for these classes.

Palabras clave

  • Sãlãgean operator
  • bi-univalent functions
  • subordination
  • shell-like curves
  • univalent functions
  • starlike functions
  • convex functions
  • Fibonacci numbers

MSC 2010

  • 30C45
  • 30C50

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