scholarly journals Quantum Hermite-Hadamard type inequalities for generalized strongly preinvex functions

2021 ◽  
Vol 6 (12) ◽  
pp. 13291-13310
Author(s):  
Humaira Kalsoom ◽  
◽  
Muhammad Amer Latif ◽  
Muhammad Idrees ◽  
Muhammad Arif ◽  
...  
Keyword(s):  
Real World ◽  
Higher Order ◽  
Integral Type ◽  
The Real ◽  
Quantum Calculus ◽  
Special Cases ◽  
Mathematical Problems ◽  
Preinvex Functions ◽  
Function Approximations ◽  
Integral Identities

<abstract><p>In accordance with the quantum calculus, the quantum Hermite-Hadamard type inequalities shown in recent findings provide improvements to quantum Hermite-Hadamard type inequalities. We acquire a new $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral identities, then employing these identities, we establish new quantum Hermite-Hadamard $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral type inequalities through generalized higher-order strongly preinvex and quasi-preinvex functions. The claim of our study has been graphically supported, and some special cases are provided as well. Finally, we present a comprehensive application of the newly obtained key results. Our outcomes from these new generalizations can be applied to evaluate several mathematical problems relating to applications in the real world. These new results are significant for improving integrated symmetrical function approximations or functions of some symmetry degree.</p></abstract>

scholarly journals Fractional Integral Inequalities for Strongly h -Preinvex Functions for a kth Order Differentiable Functions

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1448 ◽  
Author(s):  
Saima Rashid ◽  
Muhammad Amer Latif ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Integral Operator ◽  
Differentiable Function ◽  
Real World ◽  
Fractional Integral ◽  
Higher Order ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Real World Applications ◽  
Mathematical Problems ◽  
Preinvex Functions

The objective of this paper is to derive Hermite-Hadamard type inequalities for several higher order strongly h -preinvex functions via Riemann-Liouville fractional integrals. These results are the generalizations of the several known classes of preinvex functions. An identity associated with k-times differentiable function has been established involving Riemann-Liouville fractional integral operator. A number of new results can be deduced as consequences for the suitable choices of the parameters h and σ . Our outcomes with these new generalizations have the abilities to be implemented for the evaluation of many mathematical problems related to real world applications.

scholarly journals Quantum estimates in two variable forms for Simpson-type inequalities considering generalized Ψ-convex functions with applications

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 305-326
Author(s):  
Yu-Ming Chu ◽  
Asia Rauf ◽  
Saima Rashid ◽  
Safeera Batool ◽  
Y. S. Hamed
Keyword(s):  
Real World ◽  
Convex Functions ◽  
Integral Identity ◽  
Quantum Physics ◽  
Higher Order ◽  
New Approach ◽  
Quantum Calculus ◽  
Opening Up ◽  
Integral Identities

Abstract This article proposes a new approach based on quantum calculus framework employing novel classes of higher order strongly generalized Ψ \Psi -convex and quasi-convex functions. Certain pivotal inequalities of Simpson-type to estimate innovative variants under the q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral and derivative scheme that provides a series of variants correlate with the special Raina’s functions. Meanwhile, a q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral identity is presented, and new theorems with novel strategies are provided. As an application viewpoint, we tend to illustrate two-variable q ˇ 1 q ˇ 2 {\check{q}}_{1}{\check{q}}_{2} -integral identities and variants of Simpson-type in the sense of hypergeometric and Mittag–Leffler functions and prove the feasibility and relevance of the proposed approach. This approach is supposed to be reliable and versatile, opening up new avenues for the application of classical and quantum physics to real-world anomalies.

scholarly journals INVESTIGATION OF SOME RESULTS ARISING FROM POST QUANTUM CALCULUS

2020 ◽  
Vol 20 (3) ◽  
pp. 561-572
Author(s):  
GHAZALA GULSHAN ◽  
RASHIDA HUSSAIN ◽  
ASGHAR ALI
Keyword(s):  
Quantum Calculus ◽  
Special Cases ◽  
Type Integral ◽  
Integral Identities

This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and (p,q)-integrals. The purpose of this paper is to establish different type of identities for (p,q)-calculus. Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

scholarly journals Some New q—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 553 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Integral Inequalities ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Special Cases ◽  
Preinvex Functions

In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular q —integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.

scholarly journals Some Trapezium-Like Inequalities Involving Functions Having Strongly n-Polynomial Preinvexity Property of Higher Order

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Fractional Calculus ◽  
Higher Order ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions ◽  
Class Of Functions

The main objective of this paper is to introduce a new class of preinvex functions which is called as n-polynomial preinvex functions of a higher order. As applications of this class of functions, we discuss several new variants of trapezium-like inequalities. In order to obtain the main results of the paper, we use the concepts and techniques of k-fractional calculus. We also discuss some special cases of the obtained results which show that the main results of the paper are quite unifying one.

scholarly journals Conexões entre grafos e matrizes na modelagem de problemas matemáticos

2019 ◽  
Vol 40 ◽  
pp. 183
Author(s):  
Larissa Melchiors Furlan ◽  
Mylena Roehrs ◽  
Glauber Rodrigues de Quadros
Keyword(s):  
Directed Graph ◽  
Real World ◽  
Adjacency Matrix ◽  
Directed Graphs ◽  
The Real ◽  
Mathematical World ◽  
The Everyday ◽  
Mathematical Problems ◽  
Everyday Problems

Graphs theory is very important in the mathematical world as an excellent way of connecting with the real world. By using the theory of directed graphs it is possible to transform many of the everyday problems into mathematical problems, so as to make an exact study in each case. In this work we explore the matrices related to the various types of graphs, such as the vertex matrix, which is associated with a directed graph, and the adjacency matrix. Moreover, matrices of multi-step connections are constructed so as to separate the various blades between the vertices of a directed graph. Then, we will construct some applications of those results in the form of examples.

scholarly journals Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansions in the Real Domain - Part I: Scales of Regularly- or Rapidly-Varying Functions

2017 ◽  
Vol 9 ◽  
pp. 1-33 ◽  
Author(s):  
Antonio Granata
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Expansions ◽  
Higher Order ◽  
Weight Functions ◽  
Asymptotic Behaviors ◽  
The Real ◽  
Special Cases ◽  
Real Domain ◽  
The Given ◽  
Rapidly Varying Functions

In a previous series of papers we established a general theory of finite asymptotic expansions in the real domain for functions f of one real variable sufficiently-regular on a deleted neighborhood of a point x0 ∈ R, a theory based on the use of a uniquely-determined linear differential operator L associated to the given asymptotic scale and wherein various sets of asymptotic expansions are characterized by the convergence of improper integrals involving both the operator L applied to f and certain weight functions constructed by means of Wronskians of the given scale. Very special cases apart, Wronskians have quite complicated expressions and unrecognizable asymptotic behaviors; however in the present work, split in two parts, we highlight some approaches for determining the exact asymptotic behavior of a Wronskian when the involved functions are regularly- or rapidly-varying functions of higher order. This first part contains: (i) some preliminary results on the asymptotic behavior of a determinant whose entries are asymptotically equivalent to the entries of a Vandermonde determinant; (ii) the fundamental results about the asymptotic behaviors of Wronskians involving scales of functions all of which are either regularly (or, more generally, smoothly) varying or rapidly varying of a suitable higher order. A lot of examples and applications to the theory of asymptotic expansions in the real domain are given.

scholarly journals Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 51 ◽  
Author(s):  
Humaira Kalsoom ◽  
Saima Rashid ◽  
Muhammad Idrees ◽  
Yu-Ming Chu ◽  
Dumitru Baleanu
Keyword(s):  
Integral Identity ◽  
Higher Order ◽  
Integral Inequalities ◽  
Numerical Approximations ◽  
New Class ◽  
Quantum Integral ◽  
Special Cases ◽  
Preinvex Functions ◽  
Definition Of

In this paper, we present a new definition of higher-order generalized strongly preinvex functions. Moreover, it is observed that the new class of higher-order generalized strongly preinvex functions characterize various new classes as special cases. We acquire a new q 1 q 2 -integral identity, then employing this identity, we establish several two-variable q 1 q 2 -integral inequalities of Simpson-type within a class of higher-order generalized strongly preinvex and quasi-preinvex functions. Finally, the utilities of our numerical approximations have concrete applications.

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