scholarly journals Estimates of upper bound for a kth order differentiable functions involving Riemann–Liouville integrals via higher order strongly h-preinvex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shanhe Wu ◽  
Muhammad Uzair Awan ◽  
Marcela V. Mihai ◽  
Muhammad Aslam Noor ◽  
Sadia Talib
Keyword(s):  
Upper Bound ◽  
Higher Order ◽  
Differentiable Functions ◽  
Preinvex Functions

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 Inequalities for Estimations of Integrals Related to Higher-Order Strongly n -Polynomial Preinvex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yongping Deng ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Integral Identity ◽  
Higher Order ◽  
Differentiable Functions ◽  
Special Means ◽  
Preinvex Functions ◽  
New Inequalities

In this paper, we establish an integral identity associated with m -times differentiable functions. The result is then used to derive some integral estimations for higher-order strongly n -polynomial preinvex functions. Finally, we apply the obtained inequalities to construct new inequalities involving special means.

scholarly journals Estimates of Upper Bound for Differentiable Functions Associated with k-Fractional Integrals and Higher Order Strongly s-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Shanhe Wu ◽  
Muhammad Uzair Awan ◽  
Zakria Javed
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Higher Order ◽  
Fractional Integrals ◽  
Differentiable Functions ◽  
Second Derivatives ◽  
Integral Identities

In this paper, we establish two integral identities associated with differentiable functions and the k-Riemann-Liouville fractional integrals. The results are then used to derive the estimates of upper bound for functions whose first or second derivatives absolute values are higher order strongly s-convex functions.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

A Higher-Order Period Function and Its Application

2015 ◽  
Vol 25 (10) ◽  
pp. 1550140 ◽  
Author(s):  
Linping Peng ◽  
Lianghaolong Lu ◽  
Zhaosheng Feng
Keyword(s):  
Periodic Orbits ◽  
Upper Bound ◽  
Critical Period ◽  
Higher Order ◽  
Quadratic System ◽  
Critical Periods ◽  
Explicit Formulas ◽  
Period Function ◽  
Isochronous System ◽  
Isochronous Centers

This paper derives explicit formulas of the q th period bifurcation function for any perturbed isochronous system with a center, which improve and generalize the corresponding results in the literature. Based on these formulas to the perturbed quadratic and quintic rigidly isochronous centers, we prove that under any small homogeneous perturbations, for ε in any order, at most one critical period bifurcates from the periodic orbits of the unperturbed quadratic system. For ε in order of 1, 2, 3, 4 and 5, at most three critical periods bifurcate from the periodic orbits of the unperturbed quintic system. Moreover, in each case, the upper bound is sharp. Finally, a family of perturbed quintic rigidly isochronous centers is shown, which has three, for ε in any order, as the exact upper bound of the number of critical periods.

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.

Higher-order bounds on the conductivity of composites from symmetry considerations

1993 ◽  
Vol 443 (1918) ◽  
pp. 451-455 ◽  
Keyword(s):  
Upper Bound ◽  
Substantial Improvement ◽  
Higher Order ◽  
Geometric Parameters ◽  
Third Order ◽  
Symmetry Properties ◽  
Two Component ◽  
Order Bounds ◽  
Parameter Dependent ◽  
Independent Pair

It is well known that symmetry considerations can lead to improved bounds on, or even determine, the conductivity of two-component symmetric materials. The present work exploits symmetry properties to derive explicit higher-order bounds for three-component symmetric materials. The bounds contain geometric parame­ters. But even without any knowledge of these geometric parameters, substantial improvement on previous bounds is made. This is discussed in the context of equiaxed polycrystals. Results include a parameter-independent pair of bounds that for some polycrystals becomes third-order, and a parameter-dependent third-order upper bound that can be partially attained.

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 Some consequences of theories with maximal acceleration in laser–plasma acceleration

2019 ◽  
Vol 34 (15) ◽  
pp. 1950118 ◽  
Author(s):  
Ricardo Gallego Torromé
Keyword(s):  
Laser Plasma ◽  
Upper Bound ◽  
Charged Particles ◽  
Higher Order ◽  
Classical Electrodynamic ◽  
Plasma Acceleration ◽  
Maximal Acceleration ◽  
Jet Theory ◽  
Laser Plasma Acceleration

In this paper, we consider classical electrodynamic theories with maximal acceleration and some of their phenomenological consequences for laser–plasma acceleration. It is shown that in a recently proposed higher-order jet theory of electrodynamics, the maximal effective acceleration reachable by a consistent bunch of point-charged particles being accelerated by the wakefield is damped for bunches containing large number of charged particles. We argue that such a prediction of the theory is falsifiable. In the case of Born–Infeld kinematics, laser–plasma acceleration phenomenology provides an upper bound for the Born–Infeld parameter b. Improvements in the beam qualities will imply stronger constraints on b.

scholarly journals Liftings of Some Types of Tensor Fields and Connections to Tangent Bundles of pr-Velocities

1970 ◽  
Vol 40 ◽  
pp. 13-31 ◽  
Author(s):  
Akihiko Morimoto
Keyword(s):  
Vector Fields ◽  
Higher Order ◽  
Tensor Fields ◽  
Multi Index ◽  
Differentiable Functions ◽  
Tangent Bundles

In the previous paper [6], we studied the liftings of tensor fields to tangent bundles of higher order. The purpose of the present paper is to generalize the results of [6] to the tangent bundles of pr-velocities in a manifold M— notions due to C. Ehresmann [1] (see also [2]). In §1, we explain the pr-velocities in a manifold and define the (Λ)-lifting of differentiable functions for any multi-index λ -(λ1, λ2,…,λp) of non-negative integers λi satisfying ΣΛi≤r. In § 2, we construct ‹Λ›-lifts of any vector fields and ‹Λ›-lifts of 1-forms. The ‹Λ›-lift is a little bit different from the ‹Λ›-lift of vector fields in [6].

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