scholarly journals Translation, Creation and Annihilation of Poles and Zeros with the Biernacki and Ruscheweyh Operators, Acting on Meijer's G-Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Complex Plane ◽  
Convex Functions ◽  
Gamma Functions ◽  
Distribution Of Poles ◽  
Special Cases ◽  
Poles And Zeros

Meijer's G-functions are studied by the Biernacki and Ruscheweyh operators. These operators are special cases of the Erdélyi-Kober operators (for m=1). The effect of operators on Meijer's G-functions can be shown as the change in the distribution of poles and zeros on the complex plane. These poles and zeros belong to the integrand, a ratio of gamma functions, defining the Meijer's G-function. Displacement in position and increasing or decreasing in number of poles and zeroes are expressed by the transporter, creator, and annihilator operators. With special glance, three basic univalent Meijer's G-functions, Koebe, and convex functions are considered.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals New Modifications of Integral Inequalities via ℘-Convexity Pertaining to Fractional Calculus and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1753
Author(s):  
Saima Rashid ◽  
Aasma Khalid ◽  
Omar Bazighifan ◽  
Georgia Irina Oros
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Type Inequality ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Convex Mappings ◽  
Special Cases ◽  
Harmonically Convex Functions

Integral inequalities for ℘-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ℘-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are ℘-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

scholarly journals On Sherman-Steffensen type inequalities

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4627-4638 ◽  
Author(s):  
Marek Niezgoda
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Special Cases ◽  
Steffensen Inequality

In this work, Sherman-Steffensen type inequalities for convex functions with not necessarily non-negative coefficients are established by using Steffensen?s conditions. The Brunk, Bellman and Olkin type inequalities are derived as special cases of the Sherman-Steffensen inequality. The superadditivity of the Jensen-Steffensen functional is investigated via Steffensen?s condition for the sequence of the total sums of all entries of the involved vectors of coeffecients. Some results of Baric et al. [2] and of Krnic et al. [11] on the monotonicity of the functional are recovered. Finally, a Sherman-Steffensen type inequality is shown for a row graded matrix.

scholarly journals Fractional Ostrowski type inequalities for differentiable harmonically convex functions

2021 ◽  
Vol 7 (3) ◽  
pp. 3939-3958
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Special Means ◽  
Special Cases ◽  
Harmonically Convex Functions ◽  
New Inequalities

<abstract><p>In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.</p></abstract>

Circles on the Complex Plane

2021 ◽  
pp. 3-12
Author(s):  
A. Girsh
Keyword(s):  
Euclidean Space ◽  
Complex Plane ◽  
Euclidean Plane ◽  
Complex Space ◽  
Radical Center ◽  
Special Cases ◽  
Different Types ◽  
Different Dimensions ◽  
The Given ◽  
Made In

The Euclidean plane and Euclidean space themselves do not contain imaginary elements by definition, but are inextricably linked with them through special cases, and this leads to the need to propagate geometry into the area of imaginary values. Such propagation, that is adding a plane or space, a field of imaginary coordinates to the field of real coordinates leads to various variants of spaces of different dimensions, depending on the given axiomatics. Earlier, in a number of papers, were shown examples for solving some urgent problems of geometry using imaginary geometric images [2, 9, 11, 13, 15]. In this paper are considered constructions of orthogonal and diametrical positions of circles on a complex plane. A generalization has been made of the proposition about a circle on the complex plane orthogonally intersecting three given spheres on the proposition about a sphere in the complex space orthogonally intersecting four given spheres. Studies have shown that the diametrical position of circles on the Euclidean E-plane is an attribute of the orthogonal position of the circles’ imaginary components on the pseudo-Euclidean M-plane. Real, imaginary and degenerated to a point circles have been involved in structures and considered, have been demonstrated these circles’ forms, properties and attributes of their orthogonal position. Has been presented the construction of radical axes and a radical center for circles of the same and different types. A propagation of 2D mutual orthogonal position of circles on 3D spheres has been made. In figures, dashed lines indicate imaginary elements.

scholarly journals Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 117
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge Eliecer Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Special Function ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Several Variables ◽  
Special Cases ◽  
Interesting Identity ◽  
Generalized Coordinate

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

scholarly journals Hermite-Hadamard type inequalities for generalized convex functions on fractal sets style

2018 ◽  
Vol 38 (1) ◽  
pp. 101-116 ◽  
Author(s):  
Muharrem Tomar ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Special Cases ◽  
Logarithmic Means ◽  
Local Fractional Integral ◽  
Generalized Arithmetic

We aim to  establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

scholarly journals New Inequalities for Strongly r-Convex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Special Cases ◽  
Class Of Functions ◽  
New Inequalities

In this study, firstly we introduce a new concept called “strongly r-convex function.” After that we establish Hermite-Hadamard-like inequalities for this class of functions. Moreover, by using an integral identity together with some well known integral inequalities, we establish several new inequalities for n-times differentiable strongly r-convex functions. In special cases, the results obtained coincide with the well-known results in the literature.

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