scholarly journals Trapezoidal-Type Inequalities for Strongly Convex and Quasi-Convex Functions via Post-Quantum Calculus

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1238
Author(s):  
Humaira Kalsoom ◽  
Miguel Vivas-Cortez ◽  
Muhammad Amer Latif
Keyword(s):  
Convex Functions ◽  
Integral Type ◽  
Quantum Calculus ◽  
Strongly Convex ◽  
Integral Identities

In this paper, we establish new (p,q)κ1-integral and (p,q)κ2-integral identities. By employing these new identities, we establish new (p,q)κ1 and (p,q)κ2- trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results.

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 Versions of Hadamard-Type Inequalities for Strongly Exponentially α , h − m -Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Shasha Li ◽  
Ghulam Farid ◽  
Atiq Ur Rehman ◽  
Hafsa Yasmeen
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Strongly Convex ◽  
Error Estimations ◽  
Integral Identities

In this article, we prove some fractional versions of Hadamard-type inequalities for strongly exponentially α , h − m -convex functions via generalized Riemann–Liouville fractional integrals. The outcomes of this paper provide inequalities of strongly convex, strongly m -convex, strongly s -convex, strongly α , m -convex, strongly s , m -convex, strongly h − m -convex, strongly α , h − m -convex, strongly exponentially convex, strongly exponentially m -convex, strongly exponentially s -convex, strongly exponentially s , m -convex, strongly exponentially h − m -convex, and exponentially α , h − m -convex functions. The error estimations are also studied by applying two fractional integral identities.

scholarly journals Inequalities for generalized Riemann–Liouville fractional integrals of generalized strongly convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ghulam Farid ◽  
Young Chel Kwun ◽  
Hafsa Yasmeen ◽  
Abdullah Akkurt ◽  
Shin Min Kang
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Constant Multiplier ◽  
Error Estimations ◽  
Integral Identities

AbstractSome new integral inequalities for strongly $(\alpha ,h-m)$ ( α , h − m ) -convex functions via generalized Riemann–Liouville fractional integrals are established. The outcomes of this paper provide refinements of some fractional integral inequalities for strongly convex, strongly m-convex, strongly $(\alpha ,m)$ ( α , m ) -convex, and strongly $(h-m)$ ( h − m ) -convex functions. Also, the refinements of error estimations of these inequalities are obtained by using two fractional integral identities. Moreover, using a parameter substitution and a constant multiplier, k-fractional versions of established inequalities are also given.

scholarly journals Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly $ (\alpha, m) $-convex functions

2021 ◽  
Vol 6 (10) ◽  
pp. 11403-11424
Author(s):  
Ghulam Farid ◽  
◽  
Hafsa Yasmeen ◽  
Hijaz Ahmad ◽  
Chahn Yong Jung ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Strongly Convex ◽  
Increasing Functions ◽  
Integral Identities

<abstract><p>In this paper Hadamard type inequalities for strongly $ (\alpha, m) $-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly $ m $-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.</p></abstract>

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 Refinements and Generalizations of Some Fractional Integral Inequalities via Strongly Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ghulam Farid ◽  
Hafsa Yasmeen ◽  
Chahn Yong Jung ◽  
Soo Hak Shim ◽  
Gaofan Ha
Keyword(s):  
Error Bounds ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Integral Identities

In this article, we have established the Hadamard inequalities for strongly convex functions using generalized Riemann–Liouville fractional integrals. The findings of this paper provide refinements of some fractional integral inequalities. Furthermore, the error bounds of these inequalities are given by using two generalized integral identities.

scholarly journals The second Hankel determinant for strongly convex and Ozaki close-to-convex functions

2021 ◽  
Author(s):  
Young Jae Sim ◽  
Adam Lecko ◽  
Derek K. Thomas
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Univalent Functions ◽  
Inverse Function ◽  
Invariance Property ◽  
Hankel Determinant ◽  
Sharp Bounds ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Second Hankel Determinant

AbstractLet f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1 \}$$ D = { z ∈ C : | z | < 1 } , and $${{\mathcal {S}}}$$ S be the subclass of normalized univalent functions given by $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n$$ f ( z ) = z + ∑ n = 2 ∞ a n z n for $$z\in {\mathbb {D}}$$ z ∈ D . We give sharp bounds for the modulus of the second Hankel determinant $$ H_2(2)(f)=a_2a_4-a_3^2$$ H 2 ( 2 ) ( f ) = a 2 a 4 - a 3 2 for the subclass $$ {\mathcal F_{O}}(\lambda ,\beta )$$ F O ( λ , β ) of strongly Ozaki close-to-convex functions, where $$1/2\le \lambda \le 1$$ 1 / 2 ≤ λ ≤ 1 , and $$0<\beta \le 1$$ 0 < β ≤ 1 . Sharp bounds are also given for $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | , where $$f^{-1}$$ f - 1 is the inverse function of f. The results settle an invariance property of $$|H_2(2)(f)|$$ | H 2 ( 2 ) ( f ) | and $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | for strongly convex functions.

Bounds having Riemann type quantum integrals via strongly convex functions

2017 ◽  
Vol 54 (2) ◽  
pp. 221-240 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Gabriela Cristescu ◽  
Muhammad Uzair Awan
Keyword(s):  
Convex Functions ◽  
Strongly Convex Functions ◽  
Strongly Convex
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