Abstract In the article, we present several Hermite–Hadamard type inequalities for co-ordinated convex and quasi-convex functions give an application to product of moment two continuous independent random variables. Our results are generalizations some earlier results. Additionally, illustrative example on probability distribution is given support our

Several new inequalities for differentiable co-ordinated convex and concave functions in two variables which are related to the left side of Hermite- Hadamard type inequality obtained. Mathematics Subject Classification (2000): 26A51; 26D15

In the present paper, we aim to prove a new lemma and quantum Simpson’s type inequalities for functions of two variables having convexity on co-ordinates over [ α , β ] × ψ ϕ . Moreover, our deduction introduce direction as well validate previous results.

Preliminaries of q-calculus for functions two variables over finite rectangles in the plane are introduced. Some q-analogues famous Hermite–Hadamard inequality defined on presented. A q1q2-Hölder is also established to provide some quantum estimates trapezoidal type whose q1q2-partial derivatives absolute value with certain powers satisfy criteria convexity co-ordinates.

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 known classes preinvex functions. An identity associated with k-times differentiable function has been established involving integral operator. A number new can be deduced as consequences suitable choices parameters and σ . Our outcomes these have abilities implemented evaluation...

In this study, the assumption of being differentiable for convex function <i>f</i> in (<i>p</i>, <i>q</i>)-Hermite-Hadamard inequality is removed. A new identity right-hand part proved. By using established identity, some <i>q</i>)-trapezoid integral inequalities and quasi-convex functions are obtained. The presented results work extend from earlier research.

In this paper, several applications of the Hermite–Hadamard inequality for fractional integrals using GA-convexity are discussed, including some new refinements and similar extensions, as well in Gamma incomplete functions.

This paper focuses on studying the uniqueness of mild solution for an abstract fractional differential equation. We use Banach’s fixed point theorem to prove this uniqueness. Additionally, we examine stability properties equation using Ulam’s stability. To analyze these properties, consider involvement Hadamard derivatives. Throughout study, put significant emphasis role and resolvent operators. Furthermore, investigate Ulam-type by providing examples partial equations that incorporate

Abstract In this article, Hadamard-type inequalities for product of s -convex in the second sense on co-ordinates a rectangle from plane are established.

In this paper some new Hadamard-type inequalities for functions whose derivatives in absolute values are convex established. Some applications to special means of real numbers given. Finally, we also give our obtained results get error bounds the sum midpoint and trapezoidal formulae.

In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals function Υ˘ using an another ϑ(ζ˙). As additional observation, it is noted that the new class by employing ϑ(ζ˙) characterizes variety classes as special cases, which generalization previous class. Secondly, prove version Hermite-Hadamard-Fejér type inequality for h-convex functions according to Finally, ϑ(ζ˙), are establishing harmonically not previously known. Moreover, some examples...

Primordial supernovae were the first, great nucleosynthetic engines in Universe, forging elements required for later formation of planets and life. Here we show that planetesimals, precursors terrestrial planets, formed around low-mass stars debris first cosmic explosions 200 Myr after Big Bang, before galaxies far earlier than previously thought. A dense core one these collapsed to a protoplanetary disk which several Earth masses planetesimals 0.46 - 1.66 AU from their parent 0.7...

This study presents weighted trapezoidal-type inequalities for the product of two functions. While one function takes its values in Banach spaces, other complex plane. We employed technique integration by parts Bochner integrals functions variables, along with principles analysis taking productof to report our findings. In addition extension previous studies on a single variable, work generalizes results reported Dragomir whose their variables lies spaces. Our are new and original since they...

Highlighting the importance of artificial intelligence and machine learning approaches in engineering fluid mechanics problems, especially heat transfer applications is main goal presented article. With advancement Artificial Intelligence (AI) Machine Learning (ML) techniques, computational efficiency accuracy numerical results are enhanced. The theme study to use techniques examine thermal analysis MHD boundary layer flow Eyring-Powell Hybrid Nanofluid (EPHNFs) passing a horizontal cylinder...

This paper explores various Ramsey numbers associated with cycles pendant edges, including the classical number, star-critical Gallai–Ramsey and number. These play a crucial role in combinatorial mathematics, determining minimum number of vertices required to guarantee specific monochromatic substructures. We establish upper lower bounds for each these numbers, providing new insights into their behavior edges—graphs formed by attaching additional edges one or more cycle. The results...

Abstract In this paper, some refinements of Hermite–Hadamard type inequalities for GA-convex functions are obtained. Applications the obtained results to special means given.

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving established, and by using obtained identity, H?lder integral inequality geometrically-arithmetically convexity, some Fej?r type inequalities are presented. Applications our results to special means positive real numbers given as well.

In this paper, the notion of m-preinvex and (α,m)-preinvex functions is introduced then several inequalities Hermite–Hadamard type for differentiable are established.

The objective of this manuscript is to establish a link between the concept inequalities and Center-Radius order functions, which are intriguing due their properties widespread use. We introduce notion CR (Center-Radius)-order interval-valued preinvex function with help total relation two intervals. Furthermore, we discuss some new class preinvexity show that unifies several known concepts in literature also gives rise definitions. By applying these definitions, have amassed many classical...

In this paper, new Hermite-Hadamard type inequalities for n-times differentiable log-preinvex functions are established. The established results generalize some of those proved in recent papers and log-convex functions.

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form weighted fractional integral. Secondly, an integral identity and some midpoint inequalities by involving positive symmetric have been obtained. As shown, all resulting generalize several well-known inequalities, including classical Riemann–Liouville inequalities.

In this paper, we present some new and novel mappings defined over 0,1 with the help of GA-convex functions. As a consequence, obtain companions Fejér-type inequalities for functions these mappings, which provide refinements known results. The properties are discussed as well.