Explanipedia

Some New Boole-Type Inequalities via Modified Convex Functions with Their Applications and Computational Analysis Open

Talha Anwar, Abdul Mateen, Hela Elmannai, Muhammad Aamir Ali, Loredana Ciurdariu · 2025

In numerical analysis, the Boole’s formula serves as a pivotal tool for approximating definite integrals. The approximation of the definite integrals has a big role in numerical methods for differential equations; in particular, in the fin…

Hermite–Hadamard-Mercer Type Inequalities for Interval-Valued Coordinated Convex Functions Open

Muhammad Toseef, Iram Javed, Muhammad Aamir Ali, Loredana Ciurdariu · 2025

Determining the Jensen–Mercer inequality for interval-valued coordinated convex functions has been a challenging task for researchers in the fields of inequalities and interval analysis. We use ⊖g to establish the Jensen–Mercer inequality …

Generalization of Hermite–Hadamard, trapezoid, and midpoint Mercer type inequalities for fractional integrals in multiplicative calculus Open

Abdul Mateen, Zhiyue Zhang, Serap Özcan, Muhammad Aamir Ali · 2025

This study generalizes Hermite–Hadamard–Mercer type inequalities using Riemann–Liouville fractional integrals within the framework of multiplicative calculus. Multiplicative fractional integral identities are established for ∗differentiabl…

On some inequalities related to open Newton-Cotes formulas for differentiable convex functions with applications Open

Ifra Bashir Sial, Mei Sun, Muhammad Aamir Ali, Hüseyin Budak · 2025

In this paper, first, we prove a novel integral identity involving a single time-differentiable function. Then, we prove some new inequalities associated with one of the open Newton-Cotes formulas for differentiable convex functions. The n…

Generalization of some integral inequalities in multiplicative calculus with their computational analysis Open

Abdul Mateen, Zhiyue Zhang, Muhammad Aamir Ali, Mičhal Fĕckan · 2024

UDC 517.9 We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help o…

Improved Hermite–Hadamard Inequality Bounds for Riemann–Liouville Fractional Integrals via Jensen’s Inequality Open

Muhammad Aamir Ali, Wei Liu, Shigeru Furuichi, Mičhal Fĕckan · 2024

This paper derives the sharp bounds for Hermite–Hadamard inequalities in the context of Riemann–Liouville fractional integrals. A generalization of Jensen’s inequality called the Jensen–Mercer inequality is used for general points to find …

A family of quadrature formulas with their error bounds for convex functions and applications Open

Muhammad Toseef, Abdul Mateen, Muhammad Aamir Ali, Zhiyue Zhang · 2024

In numerical analysis, the quadrature formulas serve as a pivotal tool for approximating definite integrals. In this paper, we introduce a family of quadrature formulas and analyze their associated error bounds for convex functions. The ma…

Some Simpson- and Ostrowski-Type Integral Inequalities for Generalized Convex Functions in Multiplicative Calculus with Their Computational Analysis Open

Xinlin Zhan, Abdul Mateen, Muhammad Toseef, Muhammad Aamir Ali · 2024

Integral inequalities are very useful in finding the error bounds for numerical integration formulas. In this paper, we prove some multiplicative integral inequalities for first-time differentiable s-convex functions. These new inequalitie…

Generalization of Some Integral Inequalities in Multiplicative Calculus With Their Computational Analysis Open

Abdul Mateen, Zhiyue Zhang, Muhammad Aamir Ali, Mičhal Fĕckan · 2024

This paper focuses on the generalization of some multiplicative integral inequalities for twice differentiable functions. First, we derive multiplicative integral identity for multiplicatvely twice differentiable functions. Then, with the …

Hermite–Hadamard–Mercer Inequalities Associated with Twice-Differentiable Functions with Applications Open

Muhammad Aamir Ali, Thanin Sitthiwirattham, Elisabeth Köbis, Asma Hanif · 2024

In this work, we initially derive an integral identity that incorporates a twice-differentiable function. After establishing the recently created identity, we proceed to demonstrate some new Hermite–Hadamard–Mercer-type inequalities for tw…

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for s-convex functions with applications Open

Muhammad Aamir Ali, Hüseyin Budak, Sotiris K. Ntouyas, Jessada Tariboon · 2024

In this study, we use quantum calculus to prove Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in the second sense. The newly proven results are also shown to be an extension of comparable results in the literature…

Fractional Simpson's type inequalities for twice differentiable convex functions with applications Open

Jamshed Nasir, Shahid Qaisar, Saad Ihsan Butt, Muhammad Aamir Ali · 2024

In this paper, we prove a new identity involving the second derivative of the function and Riemann-Liouville fractional integrals. The newly established identity is then used to establish some new Simpson’s type inequalities for twice diff…

A new variant of Jensen inclusion and Hermite-Hadamard type inclusions for interval-valued functions Open

Ifra Bashir Sial, Mei Sun, Muhammad Aamir Ali, Hüseyin Budak · 2024

In this research, for interval-valued functions, we give a new version of Jensen inclusion which is called Jensen-Mercer inclusion. Moreover, we establish some new inclusions of Hermite-Hadamard-Mercer type for interval-valued functions.

Some Milne’s rule type inequalities for convex functions with their computational analysis on quantum calculus Open

Abdul Mateen, Zhiyue Zhang, Muhammad Aamir Ali · 2024

In this paper, we establish some new Milne?s type inequalities for the differentiable convex functions in quantum calculus (q-calculus). We prove q-integral identity first and then we prove some new Milne?s type inequalities for q-differen…

A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS Open

Thanin Sitthiwirattham, Miguel Vivas–Cortez, Muhammad Aamir Ali, Hüseyin Budak, İbrahim Avcı · 2023

In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite–Hadamard–Mercer-type inequalities fo…

New quantum Hermite–Hadamard-type inequalities for -convex functions involving recently defined quantum integrals Open

Ghazala Gulshan, Hüseyin Budak, Rashida Hussain, Muhammad Aamir Ali · 2023

UDC 517.5 We develop new Hermite–Hadamard-type integral inequalities for -convex functions in the context of -calculus by using the concept of recently defined -integrals. Then thе obtained Hermite–Hadamard inequality for -convex…

Novel q-Differentiable Inequalities Open

Xuewu Zuo, Saad Ihsan Butt, Muhammad Umar, Hüseyin Budak, Muhammad Aamir Ali · 2023

The striking goal of this study is to introduce a q-identity for a parameterized integral operator via differentiable function. First, we discover the parameterized lemma for the q-integral. After that, we provide several q-differentiable …

On Some New Maclaurin’s Type Inequalities for Convex Functions in q-Calculus Open

Thanin Sitthiwirattham, Muhammad Aamir Ali, Hüseyin Budak · 2023

This work establishes some new inequalities to find error bounds for Maclaurin’s formulas in the framework of q-calculus. For this, we first prove an integral identity involving q-integral and q-derivative. Then, we use this new identity t…

Some new parameterized Newton-type inequalities for differentiable functions via fractional integrals Open

Muhammad Aamir Ali, Christopher S. Goodrich, Hüseyin Budak · 2023

The main goal of the current study is to establish some new parameterized Newton-type inequalities for differentiable convex functions in the setting of fractional calculus. For this, first we prove a parameterized integral identity involv…

A New Version of <i>q</i>-Hermite-Hadamard’s Midpoint and Trapezoid Type Inequalities for Convex Functions Open

Muhammad Aamir Ali, Hüseyin Budak, Mičhal Fĕckan, Sundas Khan · 2023

In this paper, we establish a new variant of q -Hermite-Hadamard inequality for convex functions via left and right q -integrals. Moreover, we prove some new q -midpoint and q -trapezoid type inequalities for left and right q -differentiab…

Hermite-Hadamard Like Inequalities for Exponentially Subadditive Functions via Fractional Integrals Open

S. Abbas, Muhammad Aamir Ali, A. Hanif, Hüseyin Budak · 2023

In this work, through the Riemann-Liouville fractional integrals, we give Hermite-Hadamard type inequalities for exponentially sub-additive functions. For the product of exponentially sub-additive functions, we present fractional integral …

Study of quantum Ostrowski's-type inequalities for differentiable convex functions Open

Muhammad Aamir Ali, Mičhal Fĕckan, Abdul Mateen · 2023

UDC 517.9 We prove some new -Ostrowski's-type inequalities for differentiable and bounded functions. Moreover, we present the relationship between the newly established and already known inequalities, which is very interesting for new read…

On some new quantum trapezoid-type inequalities for q-differentiable coordinated convex functions Open

Fongchan Wannalookkhee, Kamsing Nonlaopon, Mehmet Zeki Sarıkaya, Hüseyin Budak, Muhammad Aamir Ali · 2023

On New Estimates of q-Hermite–Hadamard Inequalities with Applications in Quantum Calculus Open

Saowaluck Chasreechai, Muhammad Aamir Ali, Muhammad Amir Ashraf, Thanin Sitthiwirattham, Sina Etemad , et al. · 2023

In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Herm…

A new q-Hermite-Hadamard's inequality and estimates for midpoint type inequalities for convex functions Open

Thanin Sitthiwirattham, Muhammad Aamir Ali, Asghar Ali, Hüseyin Budak · 2023

This paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals.We also prove some new midpoint-type inequalities for q-differentiable convex functions.Moreover, we present some examples to illustrate our…

Quantum Hermite-Hadamard type inequalities and related inequalities for subadditive functions Open

Muhammad Aamir Ali, Mehmet Zeki Sarıkaya, Hüseyin Budak, Zhiyue Zhang · 2023

On inequalities of Simpson type for co-ordinated convex functions via generalized fractional integrals Open

Hasan Kara, Hüseyin Budak, Muhammad Aamir Ali · 2023

In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using the established identity, we offer some Simpson?s type inequalities for differentiable co-ordinated co…

On some error bounds of Maclaurin’s formula for convex functions in q-calculus Open

Thanin Sitthiwirattham, Muhammad Aamir Ali, Jarunee Soontharanon · 2023

. The main goal of this paper is to establish some error bounds for Maclaurin?s formula which is three point quadrature formula using the notions of q-calculus. For this, we first prove a q-integral identity involving fist time q-different…

Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions Open

Muhammad Aamir Ali, Jarunee Soontharanon, Hüseyin Budak, Thanin Sitthiwirattham, Mičhal Fĕckan · 2023

In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions.Moreover, we establish a new Simpson's type inequalities for different…

SOME BULLEN-TYPE INEQUALITIES FOR GENERALIZED FRACTIONAL INTEGRALS Open

Dafang Zhao, Muhammad Aamir Ali, Hüseyin Budak, Zai-Yin He · 2023

In this paper, we establish some new Bullen-type inequalities for differentiable convex functions using the generalized fractional integrals. The main advantage of the inequalities and operators used to obtain them is that these inequaliti…

Muhammad Aamir Ali YOU? Author Swipe