Related Experiment Video
Updated: May 1, 2026
09:39
Mapping Dysfunctional Protein-Protein Interactions in Disease
Published on: October 24, 2025
1.1K
Coefficient inequalities for a subclass of p-valent analytic functions.
Muhammad Arif1, Janusz Sokół2, Muhammad Ayaz1
1Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan.
Thescientificworldjournal
|March 28, 2014
Summary
This study investigates coefficient bounds for a new class of p-valent analytic functions. The findings generalize and extend existing results in the field of geometric function theory.
Area of Science:
- Complex Analysis
- Geometric Function Theory
Background:
- Analytic functions are fundamental in complex analysis.
- P-valent functions generalize the concept of univalent functions.
- Coefficient bounds are crucial for understanding function properties.
Purpose of the Study:
- To introduce and define a new subclass of p-valent analytic functions.
- To investigate and establish coefficient bounds for this newly defined subclass.
- To demonstrate that existing results are special cases of the new findings.
Main Methods:
- Utilizing techniques from geometric function theory.
- Applying methods for determining coefficient bounds.
- Developing new inequalities for the defined function class.
Main Results:
- Established sharp coefficient bounds for the new subclass of p-valent analytic functions.
- Demonstrated the novelty and significance of the defined subclass.
- Showcased that previously known results are particular instances of the derived bounds.
Conclusions:
- The study successfully determined coefficient bounds for a novel class of p-valent analytic functions.
- The results offer a broader perspective, encompassing and extending prior research.
- This work contributes to the advancement of geometric function theory and the study of analytic functions.
Related Concept Videos
01:28Graphical Representation of Inequalities
451
The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
451
01:29Application of Nonlinear Inequalities
357
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality: can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
357
01:30Fundamental Theorem of Algebra
503
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as: with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
503
01:23Absolute Value Inequalities
460
The absolute value is a mathematical tool that represents the distance of a number from zero on the number line, regardless of its sign. In the context of inequalities, absolute value expressions help define a range of permissible values or boundaries for a variable. These inequalities are commonly used in scientific modeling and data interpretation, where variability within or beyond a certain threshold must be captured precisely.An absolute value inequality of the form ∣x∣ ≤...
460
01:28Piecewise-Defined Functions
509
Piecewise defined functions are mathematical models where different expressions define a function over distinct intervals of the domain. These functions are useful for representing systems with varying behaviors depending on input values.For example, the function: uses a linear rule for inputs less than or equal to –1 and a quadratic rule for values greater than –1. Although it has two formulas, it still defines a single function.Another common type is the absolute value...
509
01:15Routh-Hurwitz Criterion I
751
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
751