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Papers by Ghazala Gulshan

Ukraïnsʹkij matematičnij žurnal, Sep 25, 2023

Ukrainian mathematical journal, Feb 20, 2024

Miskolc Mathematical Notes

$Research paper thumbnail of Some k-fractional associates of Hermite-Hadamard's inequality for quasi-convex functions and applications to special means$

Fractional Differential Calculus, 2017

This article brings together some inequalities associated with Hermite-Hadamard's inequality for ... more This article brings together some inequalities associated with Hermite-Hadamard's inequality for quasi-convex functions by way of k-Riemann-Liouville fractional integrals of order α. The inequalities thus obtained are applied to some special means of real numbers.

Advances in Continuous and Discrete Models

The aim of the current work is to generalize the well-known bisection method using quantum calcul... more The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for each qin(0,1)q\in (0,1)qin(0,1) q ∈ ( 0 , 1 ) is also determined. Some physical problems in engineering are resolved using the QBM technique for various values of the quantum parameter q up to three iterations to examine the validity of the method. Furthermore, it is proven that QBM is always convergent and that for each interval there exists qin(0,1)q\in (0,1)qin(0,1) q ∈ ( 0 , 1 ) for which the first approximation of root coincides with the precise solution of the problem.

Mathematics, 2022

The main objective of this study is to establish two important right q-integral equalities involv... more The main objective of this study is to establish two important right q-integral equalities involving a right-quantum derivative with parameter m∈[0,1]. Then, utilizing these equalities, we derive some new variants for midpoint- and trapezoid-type inequalities for the right-quantum integral via differentiable (α,m)-convex functions. The fundamental benefit of these inequalities is that they may be transformed into q-midpoint- and q-trapezoid-type inequalities for convex functions, classical midpoint inequalities for convex functions and classical trapezoid-type inequalities for convex functions are transformed without having to prove each one independently. In addition, we present some applications of our results to special means of positive real numbers. It is expected that the ideas and techniques may stimulate further research in this field.

Symmetry

In this investigation, we first establish new quantum Hermite–Hadamard type integral inequalities... more In this investigation, we first establish new quantum Hermite–Hadamard type integral inequalities for s-convex functions by utilizing newly defined Tq-integrals. Then, by using obtained inequality, we establish a new Hermite–Hadamard inequality for coordinated s1,s2-convex functions. The results obtained in this paper provide significant extensions of other related results given in the literature. Finally, some examples are given to illustrate the result obtained in this paper. These types of analytical inequalities, as well as solutions, apply to different areas where the concept of symmetry is important.

The aim of current study is to establish two crucial (p, q) b -integral identities for midpoint a... more The aim of current study is to establish two crucial (p, q) b -integral identities for midpoint and trapezoid type inequalities. Utilizing these identities, we developed some new variant of midpoint and trapezoid type integral inequalities of differential (α, m)-convex functions using right post quantum integral approach. Moreover, we have presented the application of derived results related to special means of positive real numbers.

Journal of Science and Arts, 2021

In this study, we obtained some new post quantum-Hermite-Hadamard inequalities for differentiable... more In this study, we obtained some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using generalized (p, q)- Hermite-Hadamard Inequality. The perseverance of this article is to establish different results on the left-hand side of (p,q)-Hermite-Hadamard inequality for differentiable convex function along with critical point. Special cases were obtained for different (p, q)-Hermite Hadamard inequalies with the critical point c for some special values of q.

Journal of Science and Arts

In this investigation, we established some new post quantum-Hermite-Hadamard inequalities for dif... more In this investigation, we established some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using the notion of 〖(p,q)〗^b-integeral .The perseverance of this article is to establish different results on the left hand side of 〖(p,q)〗^b- Hermite-Hadamard inequality for differentiable convex function along with critical a point. Some Special cases are obtain for different 〖(p,q)〗^b- Hermite Hadamard inequalies at critical point c for some specific values of q.

This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and ... more 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.