Related papers: Fekete-Szeg\"o Problem For Generalized Bi-Subordin…
We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…
The main objective of this paper is to obtain generalization of some Gruss-type inequalities in case of functional bounds by using a generalized Katugampola fractional integral.
This paper is devoted to proving the general {\L}ojasiewicz inequality, in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second…
We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)| \leq F(f,g)F(g,h) -F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Gr\"uss…
In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those…
A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is…
In this paper, first we give a new generalization of the Bohr's inequality for the class of bounded analytic functions $\mathcal{B'}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\overline{g},$…
Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this paper, we further develop the theory of generalized…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is arbitrary.
We consider multi-polylogarithm functions which are slightly different from the ordinary ones. These functions have two integral representations and an order structure similar to those of multiple zeta star values. We also give a necessary…
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.
In this article we derive some polynomial inequalities for Mertens functions.
In this work, we consider certain class of bi-univalent functions related with shell-like curves related to $\kappa-$Fibonacci numbers. Further, we obtain the estimates of initial Taylor-Maclaurin coefficients (second and third…
The present work deals with the mathematical investigation of some generalizations of the Sz\'{a}sz operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Sz\'{a}sz operators involving multiple…
In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.
In this paper we consider skew bisubmodular functions as introduced in [9]. We construct a convex extension of a skew bisubmodular function which we call Lov\'asz extension in correspondence to the submodular case. We use this extension to…
Opial's inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying generalization of Opial's inequality is presented that contains both its continuous and discrete…
The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional $p-$Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and…