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We have established this paper on m convex functions, which can be expressed as a general form of the convex function concept. First of all, some inequalities of Hadamard type are proved with fairly simple conditions. Next, an integral identity containing Atangana-Baleanu fractional integral operators is obtained to prove new inequalities for differentiable m-convex functions. Using this identity, various properties of m convex functions and classical inequalities, some new integral inequalities have been proved. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to derive some new integral inequalities related to Hermite-Hadamard type by using Riemann-Liouville fractional integral operator for the class of exponentially harmonically convex functions. The formal technique of this paper may enhance further research in this field. [ABSTRACT FROM AUTHOR]

The object of the present paper is to generalize projective curvature tensor of paraKenmotsu manifold with the help of a new generalized (0,2) symmetric tensor Z introduced by Mantica and Suh. Various geometric properties of generalized projective curvature tensor of para-Kenmotsu manifold have been studied. It is shown that a generalized projectively φ symmetric para-Kenmotsu manifold is an Einstein manifold. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, S be a multiplicatively closed subset of R, and M be an R-module. The aim of this paper is to introduce the notion of S-copure submodules and investigate some properties of this class of modules. We say that a submodule N of M is S-copure if there exists an s ∈ S such that s(N :M I) ⊆ N + (0 :M I) for every ideal I of R. [ABSTRACT FROM AUTHOR]

In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials. [ABSTRACT FROM AUTHOR]

In this paper, some new estimations of Hermite-Hadamard-Fejér type inequalities for higher order differentiable preinvex functions are established via fractional integral operators. The main motivation point of the study is that our findings, which include generalized preinvex functions for Hermite-Hadamard-Fejér type inequalities by means of fractional integral operators, are the rare results in the literature. The coincidence of the special cases of the our main theorems with the earlier works in the literature is also demonstrated as a verification of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a certain class H λ,a m,q (ξ,M) of normalized analytic functions of complex order connected with a q-analogue of integral operators. For this complex-order analytic function class, we determine a sufficient condition in terms of the coefficients, estimates for the coefficients and a maximization theorem concerning the coefficients. Various consequences and applications of our main results are also considered. A brief remark about the demonstrated equivalence of the q-calculus and the so-called (p,q)-calculus is also presented. [ABSTRACT FROM AUTHOR]

In this paper, the operator denoted by Dm : A → A, is defined by Dm[ f ](z) = (1 λ)Rm[ f ](z)+lLm[ f ](z), z 2 U, a differential-integral operator, where Rm is Ruscheweyh differential operator and Lm is Libera integral operator. By using the operator Dm the class of univalent functions denoted by M(m,λ,a), 0 ≤ λ ≤ λ 0 ≤ λ a < 1, is defined and several differential subordinations are studied. [ABSTRACT FROM AUTHOR]

Using a method proposed by T.A. Burton in [6] and Banach's Contraction Principle, we study the existence, uniqueness and approximation of the solution for a bilocal problem. We compare our results with the classical similarly results given for the Fredholm integral operator associated. The present paper extends and complements the results from [14]. [ABSTRACT FROM AUTHOR]

In this paper, we establish some sharp estimates for certain vector-valued multilinear integral operators. The operators include Littlewood-Paley operators, Marcinkiewicz operators and the Bochner-Riesz operator. As an application, we obtain the (Lp, Lq)-norm inequality for the vector-valued multilinear operators. [ABSTRACT FROM AUTHOR]

In the present paper we have proved a more general theorem dealing with ∣A, pn∣k summability by using almost increasing sequence. This theorem also includes several known results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the sharp maximal function estimates for the Toeplitz type operator related to the singular integral operator with general kernel. As an application, we obtain the boundedness of the operator on Lebesgue, Morrey and Triebel-Lizorkin spaces. [ABSTRACT FROM AUTHOR]

The authors have recently introduced a new generalized derivative operator μλ1,λ2n,m, that generalized many well-known operators. The trend of finding new differential or integral operators has attracted widespread interest. The aim of this paper is to use the relation ... to discuss some interesting results by using the technique of differential subordination. The results include both subordination and inclusion. In the case of n = 0,λ2 = 0, we obtain the results of Oros [11]. [ABSTRACT FROM AUTHOR]

In this paper, nonlocal Cauchy problems for fractional evolution equations involving Volterra-Fredholm type integral operators are investigated. Some new existence theorems of mild solutions are presented by using fractional calculus, Hölder inequality, Beta function and fixed point theorems. [ABSTRACT FROM AUTHOR]

In this paper we discuss the multilinear commutators of singular integral operators on spaces of homogeneous type. By using Hölder's inequalities and the (Lp,Lq) type boundedness of fractional integral operators on spaces of homogeneous type, we obtain that this kind of multilinear commutators is bounded from Lp to Lq, from Lp to Triebel-Lizorkin spaces and from Hb→p to Lp. We also establish their H Kq1,bα,p→, Kq2α,p) type boundedness on spaces of homogeneous type. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of nontrivial symmetric solution for the secondorder three-point boundary value problem for a function ∫ ; [0,1] × R→ R which is continuous and f (t,·) is symmetric on [0, 1]. We shall formulate conditions on ∫ which guarantee the existence of nontrivial symmetric solution. As an application, we also give some examples to demonstrate our results. [ABSTRACT FROM AUTHOR]