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This paper improves Pachpatte's results on linear integral inequalities with two variables, and gives an estimation for a general form of nonlinear integral inequality with two variables. This paper does not r...
We show that the spectral seminorm is useful to study convergence or divergence of vectorial continued fractions in Banach algebras because such convergence or divergence is related to a spectral property.
The present article investigates new classes of functions involving generalized Noor integral operator. Some properties of these functions are studied including characterization and distortion theorems. Moreov...
Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan (2003) and Pachpatte (2004). These inequalities can be used as basic tools in ...
The authors investigate various subordination results for some subclasses of analytic functions in the unit disc. We obtain some sufficient conditions for multivalent close-to-starlikeness.
We investigate the following functional inequality:
in Banach modules over a
...
The main purpose of the present paper is to establish some new sharp integral inequalities involving higher-order partial derivatives. Our results in special cases yield some of the recent results on Agarwal, ...
A second-order nonlinear differential equation, of which some solutions describe the static meniscus free surface (the static liquid bridge free surface between the shaper and the crystal surface) occurring in...
We will introduce new means of Cauchy's type
defined, for example, as
We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization p...
Jensen's Inequality on Time Scales
The theory and applications of dynamic derivatives on time scales have recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond- ...
The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space was studied. A new finite-step relaxed hybrid steepest...
By using the operator
, Definition 2.1, we introduce a class of meromorphic functions denoted by
...
We study a class of equilibrium problems which is identified with a complete metric space of functions. For most elements of this space of functions (in the sense of Baire category), we establish that the corr...
We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005). By on...
We give an improvement and a reversion of the well-known Ky-Fan inequality as well as some related results.
-Bernoulli Polynomials
In this paper, we give some further properties of
-adic
-
We establish the generalized Hyers-Ulam stability of a Pexider-type functonal equation
Let
be the Jacobi measure supported on the interval [-1, 1]. Let us introduce the Sobolev-type inner product
...
Two classes of new inequalities similar to Hardy-Hilbert inequality are showed by introducing some parameters
and two real functions
We consider a general integral operator and the class of analytic functions. We extend some univalent conditions of Becker's type for analytic functions using a general integral transform.
For
, we say
is weakly submajorized (weakly supermajorized) b...
The main purpose of this paper is to present two methods of sharpening Jordan's inequality. The first method shows that one can obtain new strengthened Jordan's inequalities from old ones. The other method sho...
Some new nonlinear retarded integral inequalities of Gronwall type are established. These inequalities can be used as basic tools in the study of certain classes of integrodifferential equations.
We consider two Pythagorean modulus introduced by Gao (2005, 2006) recently. The exact values concerning these modulus for some classical Banach spaces are determined. Some applications in geometry of Banach s...
The main object of this paper is to introduce and investigate a new subclass of normalized analytic functions in the open unit disc
whi...
We investigate an inexact proximal-type method, applied to the generalized variational inequality problem with maximal monotone operator in reflexive Banach spaces. Solodov and Svaiter (2000) first introduced ...
In a recent paper by Savaş and Şevli (2007), it was shown that each Cesáro matrix of order
, for
...
We will introduce a system of generalized implicit vector quasivariational inequalities (in short, SGIVQVI) which generalizes and unifies the system of generalized implicit variational inequalities, the system...
An equivalent linear matrix inequality (LMI) representation of bounded real lemma (BRL) for linear continuous-time systems is introduced. As to LTI system including polytopic-type uncertainties, by using a par...
Spaces in the Unit Ball
Let
be an analytic self-map and let
be a fixed analytic func...
We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert spaces. We also study th...
We solve the generalized Hyers-Ulam stability problem for multidimensional Euler-Lagrange quadratic mappings which extend the original Euler-Lagrange quadratic mappings.
-Valent Functions Defined by Multiplier Transformations
The aim of this paper is to give the radius of starlikeness of the certain classes of
-valent functions defined by multiplier transformations. T...
We prove a multiplicative inequality for inner products, which enables us to deduce improvements of inequalities of the Carlson type for complex functions and sequences, and also other known inequalities.
-Statistically Convergent Double Sequences of Fuzzy Numbers
We study the notion of
-statistically convergent for double sequence of fuzzy numbers and also get some inclusion relations.
-Integers
We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes
-integers. We investigate uniform approximation of t...
We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary
Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel fu...
and
We consider the classes
and
of the analytic functions and ...
We consider an integral operator,
, for analytic functions,
We introduce new sequence space involving lacunary sequence connected with Cesaro sequence space and examine some geometric properties of this space equipped with Luxemburg norm.
We consider the Kantorovich- and the Durrmeyer-type modifications of the generalized Favard operators and we prove an inverse approximation theorem for functions
...
We proved a new and precise inequality between the differences of power means. As a consequence, an improvement of Jensen's inequality and a converse of Holder's inequality are obtained. Some applications in p...
The norm of a Hilbert's type linear operator
is given. As applications, a new generalizations of Hilbert integral inequality, and the re...
For analytic functions
in the open unit disc
with
-Monotone Mappings
A new system of nonlinear variational inclusions involving
-monotone mappings in the framework of Hilbert space is introduced and then b...
Strong convergence theorems for approximation of common fixed points of a finite family of pseudocontractive mappings are proven in Banach spaces using an implicit iteration scheme. The results presented in th...
Let
be the unit ball in the
-dimensional complex space, for
-Laplacian
We deal with discontinuous quasilinear elliptic variational-hemivariational inequalities. By using the method of sub- and supersolutions and based on the results of S. Carl, we extend the theory for discontinu...
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