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Papers by Jesús Medina Viloria

Research paper thumbnail of Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

Hacettepe Journal of Mathematics and Statistics, 2014

Research paper thumbnail of Teorema de la curva de Jordan

Research paper thumbnail of A sandwich theorem and stability result of Hyers-Ulam type for harmonically convex functions

Research paper thumbnail of Teorema del punto fijo de Brouwer

In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Th... more In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Theorem from [3]. In this demonstration only the concept of homotopy is involved in terms of equivalence relation. Keywords: Brower Theorem, Brower Theorem, Homotop

Research paper thumbnail of Some inequalities for reciprocally (s,m)-convex in the second sense functions and applications to special means

Journal of Mathematical Inequalities, 2020

Research paper thumbnail of Sobre algunas desigualdades para funciones fuertemente convexas recíprocamente

Extracta Mathematicae, 2018

Research paper thumbnail of Sandwich theorem for reciprocally strongly convex functions

Revista Colombiana de Matemáticas, 2018

We introduce the notion of reciprocally strongly convex functions and we present some examples an... more We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

Research paper thumbnail of Jensen’s Inequality for Convex Functions on N-Coordinates

Applied Mathematics & Information Sciences, 2018

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. In this paper, we give generalization of the Jensen's inequality by using definition of convex functions on n–coordinates. Results given in [5] are particular cases of results given here.

Research paper thumbnail of Some Inequalities of Jensen Type and Lazhar Type for the Class of Harmonically and Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences, 2017

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations, in [12], Iscan gave the definition of harmonically convex functions and in [2] Bracamonte et al. extended the concept of harmonically convex functions due to Iscan, and obtained the concept of strongly reciprocally convex functions. We give some inequalities of Jensen type and Lazhar type for the class of harmonically and strongly reciprocally convex functions.

Research paper thumbnail of Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences, 2017

Research paper thumbnail of Hermite-Hadamard and Fejér type inequalities for strongly harmonically convex functions

Introducimos la noción de funciones fuertemente armónicas convexas y presentamos algunso ejemplos... more Introducimos la noción de funciones fuertemente armónicas convexas y presentamos algunso ejemplos y propiedades de ésta clase. También, establecemos algunas desigualdades del tipo Hermite-Hadamard and y Fejér para la clase introducida.We introduce the notion of strongly harmonically convex function and present some examples and properties of them. We also establish some Hermite-Hadamard and Fej\'er type inequalities for the class of strongly harmonically convex functions which generalizes previous results

Research paper thumbnail of Sandwich theorem for reciprocally strongly convex functions Teorema del Sandwich para funciones fuerte-recíprocamente convexas

Revista Colombiana de Matemáticas, 2018

We introduce the notion of reciprocally strongly convex functions and we present some examples an... more We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy f (xy/( tx + (1 − t)y)) ≤ tg (y) + (1 − t)g (x) − ct(1 − t) (1/ x − 1/ y)^ 2 , for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h (x) ≤ g (x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

Research paper thumbnail of On some Inequalities for Strongly Reciprocally Convex Functions

Research paper thumbnail of Teorema del punto fijo de Brouwer

Matemática: Una publicación de FCNM – ESPOL, 2018

In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Theore... more In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Theorem from [3]. In this demonstration only the concept of homotopy is involved in terms of equivalence relation.

Research paper thumbnail of MV3 (2018) Teorema del punto fijo de Brouwer

Research paper thumbnail of Jensen’s Inequality for Convex Functions on N-Coordinates

Applied Mathematics & Information Sciences An International Journal, 2018

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. In this paper, we give generalization of the Jensen's inequality by using definition of convex functions on n–coordinates. Results given in [5] are particular cases of results given here.

Research paper thumbnail of Some inequalities for harmonically s-convex functions

Boletín de la Asociación Matemática Venezolana, 2016

In this paper, we present some Jensen's type inequalities for harmonically s-convex functions. We... more In this paper, we present some Jensen's type inequalities
for harmonically s-convex functions. We also present some Fejer type
inequalities for the functions in that class.

Research paper thumbnail of Some Inequalities of Jensen Type and Lazhar Type for the Class of Harmonically and Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences An International Journal, 2017

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations, in [12], Iscan gave the definition of harmonically convex functions and in [2] Bracamonte et al. extended the concept of harmonically convex functions due to Iscan, and obtained the concept of strongly reciprocally convex functions. We give some inequalities of Jensen type and Lazhar type for the class of harmonically and strongly reciprocally convex functions.

Research paper thumbnail of Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences An International Journal, 2017

In this paper, we establish some new Ostrowski and Simpson type inequalities for the class of str... more In this paper, we establish some new Ostrowski and Simpson type inequalities for the class of strongly reciprocally convex functions. These bounds are very useful in applications.

Research paper thumbnail of On some Inequalities for Strongly Reciprocally Convex Functions

Extracta mathematicae, 2018

We establish some Hermite-Hadamard and Fejér type inequalities for the class of strongly reciproc... more We establish some Hermite-Hadamard and Fejér type inequalities for the class of strongly reciprocally convex functions.

Research paper thumbnail of Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

Hacettepe Journal of Mathematics and Statistics, 2014

Research paper thumbnail of Teorema de la curva de Jordan

Research paper thumbnail of A sandwich theorem and stability result of Hyers-Ulam type for harmonically convex functions

Research paper thumbnail of Teorema del punto fijo de Brouwer

In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Th... more In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Theorem from [3]. In this demonstration only the concept of homotopy is involved in terms of equivalence relation. Keywords: Brower Theorem, Brower Theorem, Homotop

Research paper thumbnail of Some inequalities for reciprocally (s,m)-convex in the second sense functions and applications to special means

Journal of Mathematical Inequalities, 2020

Research paper thumbnail of Sobre algunas desigualdades para funciones fuertemente convexas recíprocamente

Extracta Mathematicae, 2018

Research paper thumbnail of Sandwich theorem for reciprocally strongly convex functions

Revista Colombiana de Matemáticas, 2018

We introduce the notion of reciprocally strongly convex functions and we present some examples an... more We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

Research paper thumbnail of Jensen’s Inequality for Convex Functions on N-Coordinates

Applied Mathematics & Information Sciences, 2018

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. In this paper, we give generalization of the Jensen's inequality by using definition of convex functions on n–coordinates. Results given in [5] are particular cases of results given here.

Research paper thumbnail of Some Inequalities of Jensen Type and Lazhar Type for the Class of Harmonically and Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences, 2017

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations, in [12], Iscan gave the definition of harmonically convex functions and in [2] Bracamonte et al. extended the concept of harmonically convex functions due to Iscan, and obtained the concept of strongly reciprocally convex functions. We give some inequalities of Jensen type and Lazhar type for the class of harmonically and strongly reciprocally convex functions.

Research paper thumbnail of Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences, 2017

Research paper thumbnail of Hermite-Hadamard and Fejér type inequalities for strongly harmonically convex functions

Introducimos la noción de funciones fuertemente armónicas convexas y presentamos algunso ejemplos... more Introducimos la noción de funciones fuertemente armónicas convexas y presentamos algunso ejemplos y propiedades de ésta clase. También, establecemos algunas desigualdades del tipo Hermite-Hadamard and y Fejér para la clase introducida.We introduce the notion of strongly harmonically convex function and present some examples and properties of them. We also establish some Hermite-Hadamard and Fej\'er type inequalities for the class of strongly harmonically convex functions which generalizes previous results

Research paper thumbnail of Sandwich theorem for reciprocally strongly convex functions Teorema del Sandwich para funciones fuerte-recíprocamente convexas

Revista Colombiana de Matemáticas, 2018

We introduce the notion of reciprocally strongly convex functions and we present some examples an... more We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy f (xy/( tx + (1 − t)y)) ≤ tg (y) + (1 − t)g (x) − ct(1 − t) (1/ x − 1/ y)^ 2 , for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h (x) ≤ g (x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

Research paper thumbnail of On some Inequalities for Strongly Reciprocally Convex Functions

Research paper thumbnail of Teorema del punto fijo de Brouwer

Matemática: Una publicación de FCNM – ESPOL, 2018

In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Theore... more In this article we will present a brief and elegant demonstration of Brouwer's Fixed Point Theorem from [3]. In this demonstration only the concept of homotopy is involved in terms of equivalence relation.

Research paper thumbnail of MV3 (2018) Teorema del punto fijo de Brouwer

Research paper thumbnail of Jensen’s Inequality for Convex Functions on N-Coordinates

Applied Mathematics & Information Sciences An International Journal, 2018

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. In this paper, we give generalization of the Jensen's inequality by using definition of convex functions on n–coordinates. Results given in [5] are particular cases of results given here.

Research paper thumbnail of Some inequalities for harmonically s-convex functions

Boletín de la Asociación Matemática Venezolana, 2016

In this paper, we present some Jensen's type inequalities for harmonically s-convex functions. We... more In this paper, we present some Jensen's type inequalities
for harmonically s-convex functions. We also present some Fejer type
inequalities for the functions in that class.

Research paper thumbnail of Some Inequalities of Jensen Type and Lazhar Type for the Class of Harmonically and Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences An International Journal, 2017

In recent years, new classes of convex functions have been introduced in order to generalize the ... more In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations, in [12], Iscan gave the definition of harmonically convex functions and in [2] Bracamonte et al. extended the concept of harmonically convex functions due to Iscan, and obtained the concept of strongly reciprocally convex functions. We give some inequalities of Jensen type and Lazhar type for the class of harmonically and strongly reciprocally convex functions.

Research paper thumbnail of Ostrowski and Simpson Type Inequalities for Strongly Reciprocally Convex Functions

Applied Mathematics & Information Sciences An International Journal, 2017

In this paper, we establish some new Ostrowski and Simpson type inequalities for the class of str... more In this paper, we establish some new Ostrowski and Simpson type inequalities for the class of strongly reciprocally convex functions. These bounds are very useful in applications.

Research paper thumbnail of On some Inequalities for Strongly Reciprocally Convex Functions

Extracta mathematicae, 2018

We establish some Hermite-Hadamard and Fejér type inequalities for the class of strongly reciproc... more We establish some Hermite-Hadamard and Fejér type inequalities for the class of strongly reciprocally convex functions.