Skip to main content

Differential Subordinations for Non-analytic Functions | Chapter 11 | Theory and Applications of Mathematical Science Vol. 1

In paper [1], Petru T. Mocanu has obtained sufficient conditions for a function in the classes C1 (U), respectively C2 (U) to be univalent and to map U onto a domain which is starlike (with respect to origin), respectively convex. Those conditions are similar to those in the analytic case. In paper [2], Petru T. Mocanu has obtained sufficient conditions of univalency for complex functions in the class C1 which are also similar to those in the analytic case. Having those papers as inspiration, we have tried to introduce the notion of subordination for non-analytic functions of classes C1 and C2 following the classical theory of differential subordination for analytic functions introduced by S.S. Miller and P.T. Mocanu in papers [3] and [4] and developed in the book [5]. Let Ω be any set in the complex plane C, let p be a non-analytic function in the unit disc U, p ∈ C2(U) and let ψ(r, s, t; z) : C3×U → C. In article [6] we have considered the problem of determining properties of the function p, non-analytic in the unit disc U, such that p satisfies the differential subordination. ψ(p(z), Dp(z), D2p(z) − Dp(z); z) ⊂ Ω ⇒ p(U) ⊂ ∆. The present chapter is based on the results contained in paper [7], some parts of it have been removed and results obtained after the appearance of the paper have been added.

Author(s) Details

Georgia Irina Oros
Department of Mathematics and Computer Science, University of Oradea, Universitatii Street, No. 1, 410087 Oradea, Romania.

Gheorghe Oros
Department of Mathematics and Computer Science, University of Oradea, Universitatii Street, No. 1, 410087 Oradea, Romania.

View Books: http://bp.bookpi.org/index.php/bpi/catalog/book/117
Labels:

Comments

Post a Comment

Popular posts from this blog

Greening Regional Airports: A Vision for Carbon Neutral Infrastructure | Chapter 12 | Contemporary Perspective on Science, Technology and Research Vol. 3

 This study provides an overview of the energy demand of a regional airport, divided into individual time horizons. The electrification of aircraft systems raises the question of whether airports will be among the largest electricity consumers in our infrastructure in the future. Sustainability and especially emission reductions are significant challenges for airports that are currently being addressed. The Clean Sky 2 project GENESIS addresses the environmental sustainability of hybrid-electric 50-passenger aircraft systems in a life cycle perspective to support the development of a technology roadmap for the transition to sustainable and competitive electric aircraft systems. This article originates from the GENESIS research and describes various options for ground power supply at a regional airport. Potential solutions for airport infrastructure with a short (2030), medium (2040), and long (2050) time horizon are proposed. In addition to the environmental and conservation benefi...
Post a Comment
Read more

Alkali Element Modification of Glucose Molecules as a Method to Dissolve Cancer Cells | Chapter 12 | New Visions in Medicine and Medical Science Vol. 4

  The present study highlights about alkali element modification of glucose molecules as a method to dissolve cancer cells. The central regulation of the mechanisms governing cell proliferation has little effect on cancer cells. Cancer cells are entirely independent of the central command and divide and proliferate on their own, making it challenging to activate their response mechanism. Precisely, this is the reason why they are at risk to the health of humans and/or any biological entities. Instead of trying to reconnect the central command of the growth control mechanism to cancer cells that are already out of the range, we present a method of using the cancer cell’s own irresponsive and uncontrolled growth mechanism to their disadvantage and destroy the cancer cells. We found that this is achievable in an atomic/molecular level study of the glucose molecule, which is the primary food source used for growth and energy generation by all cells in the body, including the cancer cel...
Post a Comment
Read more

Occipital Dermal Sinus Tract Causing Craniospinal Infection: A Review | Chapter 13 | New Visions in Medicine and Medical Science Vol. 4

  Dermal sinus is a rare congenital condition characterized by a pathological tract connecting the skin to deeper tissues of the central nervous system, potentially leading to severe infectious complications. It arises from a failure in the separation of ectodermal layers during early gestation. Diagnosing dermal sinus tract in newborns requires a careful physical examination, focusing on midline dimples in the occipital region associated with cutaneous abnormalities like hairy nevus or hyperpigmentation. The presence of drainage, abnormal hair distribution, or localized swelling may indicate a sinus tract. Regular examination for dimples or sinuses is recommended for infants and children with recurrent meningitis or infections. Early detection is crucial to prevent severe complications like meningitis, with Staphylococcus aureus being a common causative organism. Neuroradiological studies, including computed tomography (CT) scan and magnetic resonance imaging (MRI), with histopath...
Post a Comment
Read more