There is significant interaction between the class of symmetric functions and other types functions. The multiplicative convex function class, which intimately related to idea symmetry, one them. In this paper, we obtain some new generalized fractional Hermite–Hadamard type inequalities for their product. Additionally, derive a number integrals utilising novel identity as an auxiliary result. We provide examples appropriate selections graphical representations verify authenticity our main results.

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired obtained.

This article examines the norms of composition operators from weighted harmonic Bloch space <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msubsup><a:mrow><a:mi mathvariant="script">B</a:mi></a:mrow><a:mrow><a:mi>H</a:mi></a:mrow><a:mrow><a:mi>λ</a:mi></a:mrow></a:msubsup><a:mo>,</a:mo><a:mfenced open="(" close=")"><a:mrow><a:mn>0</a:mn><a:mo>&lt;</a:mo><a:mi>λ</a:mi><a:mo>&lt;</a:mo><a:mrow><a:mo>∞</a:mo></a:mrow></a:mrow></a:mfenced></a:math> to Zygmund <f:math...

We study the Banach space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="script">B</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math> (<mml:math id="M2"><mml:mi>α</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:math>) of harmonic mappings id="M3"><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:math> on open unit disk...

For <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>α</mi> <mo>&gt;</mo> <mn>0</mn> </math> , several characterizations of the id="M2"> -Bloch spaces harmonic mappings are given. We also obtain similar for closed separable subspace. As an application, we give relations between id="M3"> <msubsup> <mrow> <mi mathvariant="script">B</mi> </mrow> <mi>H</mi> </msubsup> and Carleson’s measure.

We study the composition operators on Banach spaces of harmonic mappings that extend several well-known analytic functions open unit disk in complex plane, including α -Bloch spaces, growth Zygmund space, Besov and space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mtext>BMOA</mml:mtext></mml:mrow></mml:math>.

In this paper we study a class ${\mathcal{Z}}_{H}$ of harmonic mappings on the open unit disk $\mathbb{D}$ in complex plane that is an extension classical (analytic) Zygmund space. We extend to elements characterisation valid analytic case. also provide similar result for closed separable subspace which call little

&lt;abstract&gt;&lt;p&gt;This research paper sought to characterize the boundedness and compactness of composition operators from space $ \mathcal{H}^{\infty} bounded harmonic mappings into Zygmund \mathcal{Z}_H $, on open unit disk. Furthermore, we obtain an estimate essential norms such operator. These results extends similar that were proven for analytic function spaces.&lt;/p&gt;&lt;/abstract&gt;

In this article, we highlight a new class of salient Banach spaces on the quaternionic unit ball, so called Qp classes slice hyperholomorphic functions. We will investigate some basic results these spaces. Further, discuss invariance property concerning Mbius transformations by using an appropriate notion composition operators. It is well known that in classical functional theory received wide attention from researchers. This motivated us to examine their counterparts, as have many...

This paper examines a new class of Möbius invariant function spaces, denoted by NK(p,q)-type spaces in the unit ball Cn, which are common basis for several known holomorphic functions. We establish basic properties and its closed subspaces NK,0(p,q), Banach functions with norms determined weighted nondecreasing K:[0,∞)→[0,∞), together transformation. With Green's function, we give an equivalent description spaces. Finally, study Hadamard gap series

In this article, we introduce a new space of harmonic mappings that is an extension the well known QT in unit disk D term non decreasing function. Several characterizations QTH are investigated. We also define little subspace QTH. Finally, boundedness composition operators Cϕ mapping into and QTH,0 considered.

This paper sought to introduce a new space V H of harmonic mappings that is an extension the analytic functions whose first derivatives are in classical Zygmund space. We obtain several characterizations H. Lastly, boundedness and compactness operator Cϕ acting on investigated.