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In this paper embeddings between weighted complementary local Morrey-type spaces c LM pθ,ω (R n , v) and weighted local Morrey-type spaces LM pθ,ω (R n , v) are characterized. In particular, two-sided estimates of the optimal constant c... more
In this paper embeddings between weighted complementary local Morrey-type spaces ${\,^{^{\bf c}}\!}LM_{p\theta,\omega}({\mathbb R}^n,v)$ and weighted local Morrey-type spaces $LM_{p\theta,\omega}({\mathbb R}^n,v)$ are characterized. In... more
In this paper, the embeddings between weighted local Morrey-type spaces and weighted Lebesgue spaces are investigated. 2000 Mathematics Subject Classification. 42B35, 47B38. Key words and phrases. local Morrey-type spaces; weighted... more
We find necessary and sufficient conditions for the two-operator weighted inequality ¥ R 0 1 t t R 0 f(s)ds q w(t)dt 1/q 6C ¥ R 0 ¥ R t f(s) s ds p v(t)dt 1/p . We use this inequality to study embedding properties between the function... more
Bivariate means defined as the Schwab-Borchardt mean of two bivariate means are investigated. Explicit formulas for those means are obtained. It is demonstrated that they interpolate inequalities connecting the well known bivariate means.... more
This paper deals with the inequalities involving logarithmically convex functions of several variables. The results here provide generalizations of inequalities for univariate functions obtained by Dragomir and Dragomir and Mond.
Inequalities connecting inverse circular and inverse hyperbolic functions are obtained. Also, bounds for the inverse hyperbolic sine function are established. Some of the results presented in this paper are derived from the inequalities... more
The well-known Jensen inequality and Hermite-Hadamard inequality were extended using iterated integrals by Z. Retkes in 2008 and then by P. Kórus in 2019. In this paper, we consider analytical convex (concave) functions in order to obtain... more
For analytic functions f in the open unit disc U, a generaliza- tion operator D f(z) of Salagean operator is introduced. Some properties for D f(z) are discussed in the present paper.
We give a distortion theorem for a subclass of functions that are univalent in the unit disk, and defined using the Sˆalˆagean differential operator. The result generalizes and unifies similar well known results for several subclasses of... more
Results are obtained on existence theorems of generalized quasi-variational inequalities with monotone and lower hemi-continuous operators, or semi-monotone and upper hemicontinuous operators on paracompact sets.
Given a numerical semigroup S , a positive integer a and m ∈ S\ {0} , we introduce the set C(S, a, m) = {x ∈ N | aw(x mod m) x} , where {w(0), w(1), . . . , w(m -1)} is the Apéry set of m in S , which is a numerical semigroup and that we... more
In the article, we provide some new post quantum refinements of the Hermite-Hadamard like inequalities involving the class of h -preinvex functions by establishing a new auxiliary result involving the post quantum differentiable function.... more
Based on J. L. W. V. Jensen's concept of convex functions as well on its generalization by E. M. Wright and related to T. Popoviciu's convexity notions, higher-order convexity properties of real functions are introduced and surveyed.
Let p(z) = Pn ν=0 aνzν be a polynomial of degree n, M(p; R) := maxjzj=R≥0 jp(z)j; and M(p; 1) := M(p). Then by well-known result due to Ankeny and Rivlin [3], we have M(p:R) ≤ Rn2+ 1M(p); R ≥ 1: In this paper, we sharpen and generalizes... more
In the present paper, we establish some interesting integrals involving the product of Bessel function of the first kind with Jacobi polynomial, which are expressed in terms of Kampe de Feriet and Srivastava and Daoust functions. Some... more
In the present investigation we first introduce modified Dini function and then find sufficient conditions so that the modified Dini function have certain geometric properties like close-to-convexity, starlikeness and strongly... more
We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients.... more
We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality... more
The multiplicative sum Zagreb index is defined for a simple graph G as the product of the terms d G (u)+d G (v) over all edges uv ∈ E(G) , where d G (u) denotes the degree of the vertex u of G . In this paper, we present some lower bounds... more
The paper is dedicated to the existence of local solutions of strongly nonlinear equations in R N and the Orlicz spaces framework is used.
A real valued function f defined on a real open interval I is called Φ-convex if, for all x, y ∈ I, t ∈ [0, 1] it satisfies where Φ : R + → R + is a nonnegative error function. If f and -f are simultaneously Φ-convex, then f is said to be... more
The notion of n th order convexity in the sense of Hopf and Popoviciu is defined via the nonnegativity of the (n + 1) st order divided differences of a given real-valued function. In view of the well-known recursive formula for divided... more
A numerical semigroup is a submonoid of Z ≥0 whose complement in Z ≥0 is finite. For any set of positive integers a, b, c, the numerical semigroup S(a, b, c) formed by the set of solutions of the inequality ax mod b ≤ cx is said to be... more
A numerical semigroup is a submonoid of Z ≥0 whose complement in Z ≥0 is finite. For any set of positive integers a, b, c, the numerical semigroup S(a, b, c) formed by the set of solutions of the inequality ax mod b ≤ cx is said to be... more
Let $A$ and $B$ be $n\times n$ matrices. It is shown that if $p=2$, $4\leq p
Let A,B, and X be n × n matrices such that A,B are positive definite and X is Hermitian. If a and b are real numbers such that 0 < a s n (A) and 0 < b s n (B) , then it is shown, among other inequalities, that for every unitarily... more
We discuss the extension of inequality R A ≥ c a r b + b a r c to the plane of triangle △ABC . Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdös-Mordell inequality, and some... more
This work focuses on H and T nested functions Tpj and Hpj. We define particular nested functions based on the nested functions Tpj and Hpj and study peculiar properties of them. We propose some identities and prove important trigonometric... more
In this paper, we consider the hyperbolic Pell-Lucas sine and cosine functions. The focal point of the paper is to develop some inequalities of particular types for the hyperbolic Pell-Lucas function, including some elementary properties.
The goal of this work is to present an adapted modification to the parabolic approximation of the density function for singular integrals of Cauchy type. This approximation serves to eliminate the singularity of the integral and gives the... more
A one-parameter family of bivariate means is introduced. Members of the new family of means are derived from a bivariate symmetric mean. It is shown that new means are symmetric in their variables. Several inequalities involving... more
In this note we present a new simple and smooth transcendental approximation to f (x) = |x|, with sufficient accuracy. The proposed formula gives better approximation than x 2 + µ 2 in terms of accuracy.
In this paper, we construct the Stancu-Durrmeyer-type modification of q-Bernstein operators by means of q-Jackson integral. Here, we establish moment estimates and some direct results which include basic convergence theorem, local... more
Holder Weight Estimates of Riesz-Bessel Singular Integrals Generated by a Generalized Shift Operator
Riesz-Bessel singular integral operators generated by generalized shift operator in weighted Hölder space H γ α,β is studied. The H γ α,β boundedness of this operator is established in certain cases.
In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is... more
In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc. We also study the Hardy... more
Tavoiteltaessa vesien hyvää ekologista tilaa valuma-alueiden maankäytön ja pienvesien merkitys korostuu. Valuma-alueelta tuleva, rehevöittävä ravinnekuormitus kulkeutuu isompiin vesistöihin purojen, valtaojien ja norojen kautta. Pienet... more
In this paper we find existence results for elliptic and parabolic nonlinear variational inequalities involving a multivalued map. Both cases of a lower semicontinuous multivalued map and an upper semicontinuous one are considered.
Functional and uniform bounds for Exton's generalized hypergeometric X function of two variables and an associated incomplete Lipschitz-Hankel integral, as an auxiliary result, are obtained. A by-product for the Srivastava-Daoust... more
We explore the error of the weighted quadrature formulae and give the sufficient and necessary conditions for this type of quadrature formula to have Schur-convexity property. Some special cases of the weigted quadrature formulae are... more
In this paper the extension of the weighted Montgomery identity is established by using the integral formula of Pečarić, Matić and Ujević. Further, by using this extended weighted Montgomery identity for functions whose derivatives of... more
Let (E, ) be linearly orthogonality space, is orthogonally additive and It is proved that, under suitable assumptions on , is sublinear functional. Furthermore, if is orthogonally additive, then is continuous. (Mathematics Subject... more
In this article we find some estimations concerning convex functions in inequalities like Hermite-Hadamard inequality or Fejér inequality. Also we prove a generalization of the Hammer-Bullen inequality.
In this paper we present estimation formulas for the expectations of power means of large data and associate them with means of probability distribution and means of random sample. The proposed method follows from the asymptotic expansion... more
The paper deals with the existence and uniqueness of solutions of some non linear parabolic inequalities in the Orlicz-Sobolev spaces framework.
In this paper, we study and investigate starlikeness and convexity of a class of multivalent functions defined by a linear operator L p,k (a, c)f (z). As a consequence, a number of sufficient conditions for starlikeness and convexity of... more
Closed form expressions are obtained for a family of convergent Mathieu type a-series and its alternating variant, whose terms contain an ℵ-function, which naturally occurs in certain problems associated with driftless Fokker-Planck... more
It is well known that the quasivariational inequalities are equivalent to the fixed point problems. We use this equivalent alternative formulation to construct some merit functions for quasivariational inequalities and obtain error bounds... more