Khaled Mehrez - Academia.edu (original) (raw)

Papers by Khaled Mehrez

Journal of Difference Equations and Applications, 2017

We introduce the notion of Dunkl completely monotonic functions on (−σ, σ) , σ > 0. We establish ... more We introduce the notion of Dunkl completely monotonic functions on (−σ, σ) , σ > 0. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.

Mathematics, 2022

A variant of Jessen’s type inequality for a semigroup of positive linear operators, defined on a ... more A variant of Jessen’s type inequality for a semigroup of positive linear operators, defined on a Banach lattice algebra, is obtained. The corresponding mean value theorems lead to a new family of mean-operators.

Proceedings of NAS RA. Mathematics, 2022

In this paper, four parameters Wright function is considered. Certain geometric properties such a... more In this paper, four parameters Wright function is considered. Certain geometric properties such as starlikeness, convexity, uniform convexity and close-to-convexity are discussed for this function. Further, certain geometric properties of normalized Bessel function of the first kind and two parameters Wright function are studied as a consequence. Interesting corollaries and examples are provided to support that these results are better than the existing ones and improve several results available in the literature.

Fractal and Fractional, 2022

The main objective of this paper is to establish some sufficient conditions so that a class of no... more The main objective of this paper is to establish some sufficient conditions so that a class of normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness and k-uniform convexity are discussed for these functions. Some sufficient conditions are also derived so that these functions belong to the Hardy spaces Hp and H∞. Furthermore, the inclusion properties of some modified Mittag–Leffler-type functions are discussed. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.

arXiv: Classical Analysis and ODEs, 2015

In this paper we present several new classes of logarithmically completely monotonic functions. O... more In this paper we present several new classes of logarithmically completely monotonic functions. Our functions have in common that they are defined in terms of the q−q-q−gamma and q−q-q−digamma functions. As an applications of this results, some inequalities for the q−q-q−gamma and the q−q-q−digamma functions are established. Some of the given results generalized theorems due to Alzer and Berg and C.-P. Chen and F. Qi.

arXiv: Classical Analysis and ODEs, 2019

The purpose of this paper is to provide a set of sufficient conditions so that the normalized for... more The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. In particular, we study some geometric properties for some class of functions related to the generalized hypergeometric functions.

arXiv: Classical Analysis and ODEs, 2015

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generaliz... more In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

arXiv: Classical Analysis and ODEs, 2016

In this paper, we present a generalization of the Huygens types inequalities involving Bessel and... more In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.

arXiv: Classical Analysis and ODEs, 2015

In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel funct... more In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established

arXiv: Classical Analysis and ODEs, 2020

The main focus of the present paper is to investigate several generating functions for a certain ... more The main focus of the present paper is to investigate several generating functions for a certain classes of functions associated to the Fox-Wright functions. In particular, certain generating functions for a class of function involving the Fox-Wright functions will be expressed in terms of the H-function of two variables are investigated. As applications, some generating functions associated to the generalized Mathieu type power series and the extended Hurwitz-Lerch zeta function are established. Furthermore, some new double series identity are considered. A conjecture about the finite Laplace transform of a class of function associated to the Fox's H-function is made.

Journal of The Korean Mathematical Society, 2021

The main focus of the present paper is to present new set of sufficient conditions so that the no... more The main focus of the present paper is to present new set of sufficient conditions so that the normalized form of the Mittag-Leffler and Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disk. Interesting consequences and examples are derived to support that these results are better than the existing ones and improve several results available in the literature.

arXiv: Classical Analysis and ODEs, 2018

In this present investigation, we found a set of sufficient conditions to be imposed on the param... more In this present investigation, we found a set of sufficient conditions to be imposed on the parameters of the Fox H-functions which allow us to conclude that it is non-negative. As applications, various new facts regarding the Fox-Wright functions, including complete monotonicity, logarithmic completely monotonicity and monotonicity of ratios are considered.

Journal of Mathematical Inequalities, 2021

The main focus of the present paper is to establish definite integral formulae for ratios of the ... more The main focus of the present paper is to establish definite integral formulae for ratios of the Fox-Wright functions. As consequences of the master formula, some novel integral formulae are derived for ratios of other special functions which are associated to Fox-Wright Ψ function, like generalized hypergeometric function, modified Bessel function of the first kind and Mittag-Leffler type functions of two and three parameters. Moreover, closed integral form expressions are obtained for a family of Mathieu-type series and for the associated alternating versions whose terms contain the incomplete Fox-Wright function. As applications, functional bounding inequalities are established for the aforementioned series.

Integral Transforms and Special Functions, 2018

In this paper we prove some monotonicity, log-convexity and log-concavity properties for the Volt... more In this paper we prove some monotonicity, log-convexity and log-concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Turán type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.

Journal of Mathematical Analysis and Applications, 2018

Our aim in this paper is to derive several new integral representations of the Fox-Wright functio... more Our aim in this paper is to derive several new integral representations of the Fox-Wright functions. In particular, we give new Laplace and Stieltjes transform for this special functions under a special restriction on parameters. From the positivity conditions for the weight in these representations, we found sufficient conditions to be imposed on the parameters of the Fox-Wright functions that it be completely monotonic. As applications, we derive a class of function related to the Fox H-functions is positive definite and an investigation of a class of the Fox H-function is non-negative. Moreover, we extended the Luke's inequalities and we establish a new Turán type inequalities for the Fox-Wright function. Finally, by appealing to each of the Luke's inequalities, two sets of two-sided bounding inequalities for the generalized Mathieu's type series are proved.

Journal of Inequalities and Applications, 2019

Our aim in this present paper is to establish several Chebyshev type inequalities involving gener... more Our aim in this present paper is to establish several Chebyshev type inequalities involving generalized fractional conformable integral operator recently introduced by T.U. Khan and M.A. Khan (J. Comput. Appl. Math. 346:378–389, 2019). Also, we present Chebyshev type inequalities involving Riemann–Liouville type fractional conformable integral operators as a particular result of our main result.

Mathematical Inequalities & Applications, 2019

In this paper our aim is to present the completely monotonicity and convexity properties for the ... more In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and log-convexity results for the generalized Wright functions. As applications, we present several new inequalities (like Turán type inequalities) and we prove some geometric properties for four-parametric Mittag-Leffler functions.

Positivity, 2018

In this paper we give some conditions for a class of functions related to Bessel functions to be ... more In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite. We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions.

Applicable Analysis and Discrete Mathematics, 2019

Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu... more Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu-type power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of these special function. Moreover, we introduce the notion of the (p, q)-Mittag- Leffler functions and we present a relationships between these two functions. Some other applications are proved, in particular two Tur?n type inequalities for the (p,q)-Mathieu-type series are derived.

Mathematics, 2019

In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermi... more In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.

Journal of Difference Equations and Applications, 2017

We introduce the notion of Dunkl completely monotonic functions on (−σ, σ) , σ > 0. We establish ... more We introduce the notion of Dunkl completely monotonic functions on (−σ, σ) , σ > 0. We establish a restrictive version of the analogue of Schoenberg's theorem in Dunkl setting.

Mathematics, 2022

A variant of Jessen’s type inequality for a semigroup of positive linear operators, defined on a ... more A variant of Jessen’s type inequality for a semigroup of positive linear operators, defined on a Banach lattice algebra, is obtained. The corresponding mean value theorems lead to a new family of mean-operators.

Proceedings of NAS RA. Mathematics, 2022

In this paper, four parameters Wright function is considered. Certain geometric properties such a... more In this paper, four parameters Wright function is considered. Certain geometric properties such as starlikeness, convexity, uniform convexity and close-to-convexity are discussed for this function. Further, certain geometric properties of normalized Bessel function of the first kind and two parameters Wright function are studied as a consequence. Interesting corollaries and examples are provided to support that these results are better than the existing ones and improve several results available in the literature.

Fractal and Fractional, 2022

The main objective of this paper is to establish some sufficient conditions so that a class of no... more The main objective of this paper is to establish some sufficient conditions so that a class of normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness and k-uniform convexity are discussed for these functions. Some sufficient conditions are also derived so that these functions belong to the Hardy spaces Hp and H∞. Furthermore, the inclusion properties of some modified Mittag–Leffler-type functions are discussed. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.

arXiv: Classical Analysis and ODEs, 2015

In this paper we present several new classes of logarithmically completely monotonic functions. O... more In this paper we present several new classes of logarithmically completely monotonic functions. Our functions have in common that they are defined in terms of the q−q-q−gamma and q−q-q−digamma functions. As an applications of this results, some inequalities for the q−q-q−gamma and the q−q-q−digamma functions are established. Some of the given results generalized theorems due to Alzer and Berg and C.-P. Chen and F. Qi.

arXiv: Classical Analysis and ODEs, 2019

The purpose of this paper is to provide a set of sufficient conditions so that the normalized for... more The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disc. In particular, we study some geometric properties for some class of functions related to the generalized hypergeometric functions.

arXiv: Classical Analysis and ODEs, 2015

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generaliz... more In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

arXiv: Classical Analysis and ODEs, 2016

In this paper, we present a generalization of the Huygens types inequalities involving Bessel and... more In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.

arXiv: Classical Analysis and ODEs, 2015

In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel funct... more In this paper, new sharpened Huygens type inequalities involving Bessel and modified Bessel functions of the first kinds are established

arXiv: Classical Analysis and ODEs, 2020

The main focus of the present paper is to investigate several generating functions for a certain ... more The main focus of the present paper is to investigate several generating functions for a certain classes of functions associated to the Fox-Wright functions. In particular, certain generating functions for a class of function involving the Fox-Wright functions will be expressed in terms of the H-function of two variables are investigated. As applications, some generating functions associated to the generalized Mathieu type power series and the extended Hurwitz-Lerch zeta function are established. Furthermore, some new double series identity are considered. A conjecture about the finite Laplace transform of a class of function associated to the Fox's H-function is made.

Journal of The Korean Mathematical Society, 2021

The main focus of the present paper is to present new set of sufficient conditions so that the no... more The main focus of the present paper is to present new set of sufficient conditions so that the normalized form of the Mittag-Leffler and Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disk. Interesting consequences and examples are derived to support that these results are better than the existing ones and improve several results available in the literature.

arXiv: Classical Analysis and ODEs, 2018

In this present investigation, we found a set of sufficient conditions to be imposed on the param... more In this present investigation, we found a set of sufficient conditions to be imposed on the parameters of the Fox H-functions which allow us to conclude that it is non-negative. As applications, various new facts regarding the Fox-Wright functions, including complete monotonicity, logarithmic completely monotonicity and monotonicity of ratios are considered.

Journal of Mathematical Inequalities, 2021

The main focus of the present paper is to establish definite integral formulae for ratios of the ... more The main focus of the present paper is to establish definite integral formulae for ratios of the Fox-Wright functions. As consequences of the master formula, some novel integral formulae are derived for ratios of other special functions which are associated to Fox-Wright Ψ function, like generalized hypergeometric function, modified Bessel function of the first kind and Mittag-Leffler type functions of two and three parameters. Moreover, closed integral form expressions are obtained for a family of Mathieu-type series and for the associated alternating versions whose terms contain the incomplete Fox-Wright function. As applications, functional bounding inequalities are established for the aforementioned series.

Integral Transforms and Special Functions, 2018

In this paper we prove some monotonicity, log-convexity and log-concavity properties for the Volt... more In this paper we prove some monotonicity, log-convexity and log-concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Turán type inequalities) as well as we determined sharp upper and lower bounds for the normalized incomplete Volterra functions in terms of weighted power means.

Journal of Mathematical Analysis and Applications, 2018

Our aim in this paper is to derive several new integral representations of the Fox-Wright functio... more Our aim in this paper is to derive several new integral representations of the Fox-Wright functions. In particular, we give new Laplace and Stieltjes transform for this special functions under a special restriction on parameters. From the positivity conditions for the weight in these representations, we found sufficient conditions to be imposed on the parameters of the Fox-Wright functions that it be completely monotonic. As applications, we derive a class of function related to the Fox H-functions is positive definite and an investigation of a class of the Fox H-function is non-negative. Moreover, we extended the Luke's inequalities and we establish a new Turán type inequalities for the Fox-Wright function. Finally, by appealing to each of the Luke's inequalities, two sets of two-sided bounding inequalities for the generalized Mathieu's type series are proved.

Journal of Inequalities and Applications, 2019

Our aim in this present paper is to establish several Chebyshev type inequalities involving gener... more Our aim in this present paper is to establish several Chebyshev type inequalities involving generalized fractional conformable integral operator recently introduced by T.U. Khan and M.A. Khan (J. Comput. Appl. Math. 346:378–389, 2019). Also, we present Chebyshev type inequalities involving Riemann–Liouville type fractional conformable integral operators as a particular result of our main result.

Mathematical Inequalities & Applications, 2019

In this paper our aim is to present the completely monotonicity and convexity properties for the ... more In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and log-convexity results for the generalized Wright functions. As applications, we present several new inequalities (like Turán type inequalities) and we prove some geometric properties for four-parametric Mittag-Leffler functions.

Positivity, 2018

In this paper we give some conditions for a class of functions related to Bessel functions to be ... more In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite. We present some properties and relationships involving logarithmically completely monotonic functions and strictly positive definite functions. In particular, we are interested with the modified Bessel functions.

Applicable Analysis and Discrete Mathematics, 2019

Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu... more Our aim in this paper, is to establish certain new integral representations for the (p,q)-Mathieu-type power series. In particular, we investigate the Mellin-Barnes type integral representations for a particular case of these special function. Moreover, we introduce the notion of the (p, q)-Mittag- Leffler functions and we present a relationships between these two functions. Some other applications are proved, in particular two Tur?n type inequalities for the (p,q)-Mathieu-type series are derived.

Mathematics, 2019

In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermi... more In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.