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A. M. Mercer prove a new version of well-known Jensen inequality which is called Jensen-Mercer inequality [16]. By using Jensen-Mercer inequality, Kian andMoslehian establish a new variant of Hermite-Hadamard inequality which is called Hermite-Jensen-Mercer inequality [15]. In this paper, we extend the Hermite-Jensen-Mercer inequality for quantum integrals by utilizing Jensen-Mercer inequality. Then we investigate the connections between our results and those in earlier works. Moreover we give some examples to illustrate the main results in this paper. This is the first paper focusing on Hermite-Jensen-Mercer inequalities for quantum integrals. [ABSTRACT FROM AUTHOR]

In this paper, we consider norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series for the Walsh system. We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the following two-dimesional system of difference equations ... where the parameters a;b; c;d and the initial values x i; y i, i 2 f1;2;3;4;5;6g, are real numbers. We show that some subclasses of nonlinear two-dimensional system of difference equations are solvable in closed form. We also describe the forbidden set of solutions of the system of differ- ence equations. Some numerical examples are given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912-3919, 2011]. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new function class called n-fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n-fractional polynomial convex. Also, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]

In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature rela- tions between the total space, the base space and the fibres on a submersion. In the present paper, we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. [ABSTRACT FROM AUTHOR]

In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

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]

In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

In 2004, Patrício and Puystjens characterized the relation between Drazin invertible elements (resp., Moore-Penrose invertible elements) of two semigroups pRp and pRp+1 p of a ring R for some idempotent (resp., projection) p ∈ R. In this paper, we consider the relevant result for pseudo core invertible elements of such two semigroups of a ring for some projection, which is then applied to characterize the relation between pseudo core invertible elements of the matrix semigroup AA†RmxmAA†+Im AA† and the matrix semigroup A†ARnxnA†A+In A†A, where A ∈ Rmxn with A† existing. Also, similar equivalence involving DMP invertible elements is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we have proved certain kinds of Tauberian theorems for Nörlund-Cesáro summability methods in m-normed space X in statistically sense. We give necessary and sufficient Tauberian condition for this method of summability, in statistically sense. Also, we prove that Tauberian theorems under these summability methods are valid under oscillating slow condition of Schmidt-type and Hardy-type conditions. [ABSTRACT FROM AUTHOR]

In the present paper, we characterize Lie (Jordan) σ-centralizers of generalized matrix algebras. More precisely, we obtain some conditions under which every Lie σ-centralizer of a generalized matrix algebra can be expressed as the sum of a σ-centralizer and a center- valued mapping. Further, it is shown that under certain appropriate assumptions every Jordan σ-centralizer of a generalized matrix algebra is a σ-centralizer. Finally, the main results are applied to triangular algebras. [ABSTRACT FROM AUTHOR]

In the present paper, we study the existence of at least one weak solution for a class of double phase variable exponent problem with a reaction term depending on the gradient and on two real parameters. By using the topological degree theory for a class of demicontinuous operators of generalized (S+) and the theory of the variable exponent Sobolev spaces, we obtain the existence of at least one weak solution of this problem. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the feedback control systems governed by Hilfer fractional evolution inclusions involving history-dependent operators. We first show a priori estimates of the solutions to the fractional feedback control system. Then, by using the well-known Bohnenblust-Karlin fixed point theorem, we prove an existence theorem for the fractional feedback control system. Finally, we consider an optimal control problem driven by the fractional feedback control system, and establish its solvability. [ABSTRACT FROM AUTHOR]

The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley. [ABSTRACT FROM AUTHOR]

The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]

Let R be a prime ring, I be a nonzero ideal of R, Q be its maximal right ring of quotients and C be its extended centroid. The aim of this paper is to show that if R admits a nonzero b-generalized derivation F such that [F (xm)xn + xnF (xm), xr]k = 0 for all x ∈ I, where m, n, r, k are fixed positive integers, then there exists λ ∈ C such that F (x) = λx unless R ∼= M2(GF(2)), the 2 × 2 matrix ring over the Galois field GF(2) of two elements. [ABSTRACT FROM AUTHOR]

This paper is concerned with sharp solutions to majorization and Fekete-Szegő problems for several relatively new normalized subfamilies of starlike functions. Regarding starlike functions which are subordinated to Sine and Cosine functions, a number of new results are established. The results provide improvements to some recent results. As applications, some interesting deductions are also listed. The findings of this study are thoroughly supported by examples wherever necessary. [ABSTRACT FROM AUTHOR]

In this paper, our main focus is to establish complete monotonicity properties, convexity properties and some interesting inequalities for the Barnes Mittag-Leffler function. Furthermore, monotonicity properties of ratios of Barnes Mittag-Leffler functions are derived. Moreover, Tur´an type inequalities and several new inequalities are obtained for this function as application. Results obtained in this work are new and their importance is illustrated by several attractive consequences and corollaries. [ABSTRACT FROM AUTHOR]

n this paper we introduce the concepts of Wijsman ρ-statistical convergence of order α and Wijsman strongly ρ-convergence of order α. In addition, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

A ring R is said to be n-fine if every nonzero element in R can be written as a sum of a nilpotent and n units in R. The class of these rings contains fine rings and n-good rings in which each element is a sum of n units. Fundamental properties of such rings are obtained. One of the main results of this paper is that the m × m matrix ring Mm(R) over any arbitrary ring R is 2-fine. Furthermore, the m × m matrix ring Mm(R) over a n-fine ring R is n-fine. [ABSTRACT FROM AUTHOR]

The paper introduces the notions of boundedness and convergence with speed for difference sequences, and characterizes certain matrix classes associating the sets of such classes of sequences involving the operator Δ and two speeds λ = (λk) and µ = (µk) ... The results obtained in this paper should easily extendible to difference sequences of higher orders, and even, in combination with multipliers. [ABSTRACT FROM AUTHOR]

In this paper, some existence results for generalized vector equilibrium-like problems (for short, GVELPs) are established by virtue of a generalized KKM-Fan theorem in topological vector spaces. In addition, some applications to vector optimization problems are also given. The results presented in this paper are the extension and improvement of the corresponding results of other authors. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself is equal to a given element of the ring. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the additive (α, β)-functional equation ... for all complex numbers α with [α] D 1 and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α, β)-functional equation (0.1) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper we determine distance k--domination number of graph obtained by duplication of vertices altogether by edges in cycle Cn, splitting graph of cycle Cn as well as graph obtained by duplication of edges altogether by vertices in cycle Cn. [ABSTRACT FROM AUTHOR]

In this paper we propose a parallel iterative hybrid methods for finding a common element of the solution sets of a finite family of pseudomonotone equilibrium problems and the fixed points set of a semigroup-nonexpensive mappings in Hilbert spaces. Under mild conditions, we obtain the strong convergence of the proposed iterative process. Some numerical experiments are given to verify the efficiency the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we obtain some Cheeger-Gromov-Taylor type compactness theorems for a forward complete and connected Finsler manifold of dimensional n ≥ 2 via weighted Ricci curvatures. The proofs are based on the index form of a minimal unit speed geodesic segment, Bochner-Weitzenböck formula and Hessian comparison theorem. [ABSTRACT FROM AUTHOR]

In this paper we discuss the approach for optimal switching control problem with unknown switching points. The case with unknown switching point is more general and generalizes the results existing in the literature. By using suitable transformation, the main problem is reduced into a problem with known interval and further the unknown boundary of the integral in the minimization functional is reduced to the known one. This fact is illustrated by an example. The reduced problem is solved numerically by using the Gradient Projection Method Algorithm. [ABSTRACT FROM AUTHOR]

The number of formal concepts generated from the input context is an important parameter in the cost functions of concept formation algorithms. The calculation of concept count for any arbitrary context is a hard, NP-complete problem and only rough approximation methods can be found in the literature to solve this problem. This paper introduces an efficient numerical approximation algorithm for contexts where attribute probabilities are independent from the objects instances. The preconditions required by the approximation method are usually met in the FCA applications, thus the proposed method provides an efficient tool for practical complexity analysis, too. [ABSTRACT FROM AUTHOR]

In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejér inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard- Fejer inequality and better than given in [9] by Sarıkaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kırmacı. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a pair (f, h) called upper class of type II and αβ-contractive mappings. We obtain that all the corresponding established results of Hussain et al. [7] are immediately consequences of our main result. Our main result generalizes and modifies several existing results in literature. Also, an example is given to support the main result. [ABSTRACT FROM AUTHOR]

Let n ≥ 1 be a fixed positive integer and R be a ring. A permuting n-additive map Ω : Rn → R is known to be permuting generalized n-derivation if there exists a permuting n-derivation Δ : Rn → R such that Ω(x1, x2, ⋯,xixi⋯,xn) = Ω(x1, x2, ⋯,xi,⋯xn)xi + xi Δ(x1, x2, ⋯,xi⋯xn) holds for all xi, xi ∈ R. A mapping δ : R → R defined by δ(x) = Δ(x, x, ⋯, x) for all x ∈ R is said to be the trace of Δ. The trace &# of can be defined in ω of Ω can be defined in the similar way. The main result of the present paper states that if R is a (n+1)!-torsion free semi-prime ring which admits a permuting n-derivation Δ such that the trace δ of Δ satisfies [[δ(x), x], x] ∈ Z (R) for all x ∈ R, then ͐ is commuting on R. Besides other related results it is also shown that in a n-torsion free prime ring if the trace ω of a permuting generalized n-derivation is centralizing on R, then ω is commuting on R. [ABSTRACT FROM AUTHOR]

In this paper, we generalize β* relation on submodules of a module (see [1]) to elements of a complete modular lattice. Let L be a complete modular lattice. We say a;b ∊ L are β* equivalent , aβ*b, if and only if for each t ∊ L such that a⋁t = 1 then b⋁t = 1 and for each k ∊ L such that b⋁k D1 then a⋁k D1, this is equivalent to a⋁b⪡1=a and a⋁b⪡1=b. We show that the β* relation is an equivalence relation. Then, we examine β* relation on weakly supplemented lattices. Finally, we show that L is weakly supplemented if and only if for every x ∊ L, x is equivalent to a weak supplement in L. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe the solution (f,g) of the equation = , x,y ∣ X, where f:X→Y , g:X→X, X,Y are inner product spaces over the same field K ∣ {R,C}. [ABSTRACT FROM AUTHOR]

In this paper, the order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials (q > 0) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∊ C : ∣z∣ < R}, R > q, the rate of approximation by the q- Durrmeyer - Stancu operators (q > 1) is of order q-n versus 1/n for the classical q-Durrmeyer - Stancu operators. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the double inequality Mα(a,b) < NGQ(a,b) 0 with a ≠ b if and only if α ≤ 2log2/(5log2-2logπ) = 1:1785... and β ≥ 4/3,where NGQ(a,b) = [G(a,b)CQ2(a,b)=U(a,b)]/2 is the second Neuman mean, G(a,b) = √ab, Q(a,b) = √(a2+b2)/2 and U(a,b) = (a-b)/[√2tan-1((a - b)/ √2ab)] are the geometric, quadratic and Yang mean of a and b, respectively( [ABSTRACT FROM AUTHOR]

In this paper, we show that there is no solution of the diophantine equation uk1+ uk2 +...+ukn-1 = uln+1+uln+2+...+uln+rr for special cases of k and l where the elements of sequence fung satisfy the relation un = Aun-1 - un-2 with u0 = 0, u1= 1 and A ≥ 3 is a positive integer. [ABSTRACT FROM AUTHOR]

A graph G is called a fractional ID-k-factor-critical graph if after deleting any independent set of G the resulting graph admits a fractional k-factor. In this paper, we prove that for k≥2, G is a fractional ID-k-factor-critical graph if δ(G) ≥n/3+k,σ2(G)≥4n/3,n≥6k-8 The result is best possible in some sense. [ABSTRACT FROM AUTHOR]

Let R be a ring and M be a left R-module. M is called cofinitely weak δ-supplemented (or briefly δ- CWS-module) if every cofinite submodule of M has a weak δ-supplement in M. In this paper, we give various properties of this kind of modules. It is shown that a module M is δ-CWS-module if and only if every maximal submodule has a weak δ-supplement in M. The class of cofinitely weak δ-supplemented modules are closed under taking homomorphic images, arbitrary sums and short exact sequences. Also we give some conditions equivalent to being a δ-CWS-module for a δ-coatomic module. [ABSTRACT FROM AUTHOR]

In this paper, an effort has been made to improve the notion of α-Geraghty contraction type mappings and establish some common fixed point theorems for a pair of α-admissible mappings under the improved approach of generalized rational α-Geraghty contractive type condition in a complete metric space. An example has been constructed to demonstrate the novelty of these results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new look at Finsler surfaces. Landsberg surfaces are Finsler surfaces that are solutions of a system of non-linear partial differential equations. Considering the unicorn’s Landsberg problem, we reduce this system to a single non-linear PDE which we call the Landsberg’s PDE. By making use of the new look of Finsler surfaces, we solve the Landsberg’s PDE and get a class of solutions. Moreover, we show that these solutions and their conformal transformations are Berwaldain.

In this paper, we introduce the concept of the statistical convergence with respect to solid topology and Riesz valued norms on lattice-normed locally solid Riesz spaces. Moreover, we give the notions of statistically pτpτpτpτ

In the present paper, we give the bounds for the second Hankel determinant of the logarithmic coefficients of a certain subclass of normalized univalent functions, which we have introduced here. Relevant connections of the results, which we have presented here, with those available in the existing literature are also described briefly.