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In this paper, we consider the class of p-convex functions. We derive some new integral inequalities of Hermite-Hadamard and Simpson type for differentiable p-convex functions using two new integral identities. Some special cases are also discussed. Interested readers may find novel and innovative applications of p-convex functions in various branches of pure and applied sciences. The ideas and techniques of this paper may stimulate further research in this field.

In this paper, we show that the generalized Aluthge transformations of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operatorMwEMu is p-hyponormal if and only if it is normal, and under a weak condition, if MwEMu is normal, then the Holder inequality turn into equality for w; u. Also, we give some applications of p-hyponormal weighted conditional type operators, for instance, point spectrum and joint point spectrum of p-hyponormal weighted conditional type operators are equal. In the end, some examples are provided to illustrate concrete application of the main results of the paper. This article has been retracted. Link to the retraction 10.2298/FIL1601253E

In this paper, two kinds of system of fuzzy differential inclusions are introduced and studied. An existence of the solutions for one system of fuzzy differential inclusions is proved by using continuous selection theorem. An existence of the solutions for another system of fuzzy differential inclusions is also proved by employing the fixed point theorem in the generalized metric space. The results presented in this paper improve and extend some known results concerned with the multivalued Cauchy problem and fuzzy differential inclusions.

In this paper, new Hermite-Hadamard type inequalities for n-times differentiable log-preinvex functions are established. The established results generalize some of those results proved in recent papers for differentiable log-preinvex functions and differentiable log-convex functions.

Vanishing of linearly independent curvature tensors of a non-symmetric affine connection space as functions of vanished curvature tensor of the associated space of this one are analyzed in the first part of this paper. Projective curvature tensors of a non-symmetric affine connection space are expressed as functions of the affine connection coefficients and Weyl projective tensor of the corresponding associated affine connection space in the second part of this paper.

In this paper we study the notion of a graded $\Omega$-group $(X,+,\Omega),$ but graded in the sense of M.~Krasner, i.e., we impose nothing on the grading set except that it is nonempty, since operations of $\Omega$ and the grading of $(X,+)$ induce operations (generally partial) on the grading set. We prove that graded $\Omega$-groups in Krasner's sense are determined up to isomorphism by their homogeneous parts, which, with respect to induced operations, represent partial structures called $\Omega$-\emph{homogroupoids}, thus narrowing down the theory of graded $\Omega$-groups to the theory of $\Omega$-homogroupoids. This approach already proved to be useful in questions regarding A. V. Kelarev's $S$-graded rings inducing $S,$ where $S$ is a partial cancellative groupoid. Particularly, in this paper we prove that the homogeneous subring of a Jacobson $S$-graded ring inducing $S$ is Jacobson under certain assumptions. We also discuss the theory of prime radicals for $\Omega$-homogroupoids thus extending results of A.~V.~Mikhalev, I.~N.~Balaba and S.~A.~Pikhtilkov in a natural way. We study some classes of $\Omega$-homogroupoids for which the lower and upper weakly solvable radicals coincide and also, study the question of the homogeneity of the prime radical of a graded ring.

Motivated by a recent paper, in which the authors studied Re-nnd {1,3}-inverse, {1,4}-inverse and {1,3,4}-inverse of a square matrix, in this paper, we establish some equivalent conditions for the existence of Re-nnd {1,2,3}-inverse, {1,2,4}-inverse and {1,3,4}-inverse. Furthermore, some expressions of these generalized inverses are presented.

In this paper, we mainly give much simple proof to Theorem 1.1 and (1.6) of Theorem 1.2 posed in the paper ?F. Qi, Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities, Filomat 27 (2013) 601-604.?

In this paper, we study the symmetric generalized quasi-variational inclusion problems. Then, we establish some existence theorems of solution sets for these problems. Moreover, the stability of solutions for these problems are also onbtained. Finally, we apply these results to symmetric vector quasi-equilibrium problems. The results presented in this paper improve and extend the main results in the literature. Some examples are given to illustrate our results.

In this paper we point out that a number of fixed point papers, involving several maps, are special cases of a general result proved several years ago by the author and G. F. Jungck, and one proved by Aliouche and Popa [1].

In this paper, we introduce and investigate three interesting subclass $\Sigma_\vartheta^*(\lambda,\alpha)$, $\Sigma_\vartheta^B(\beta,\alpha)$ and $\tilde{\Sigma}_\vartheta^*(\alpha,\beta)$ of meromorphic and bi-univalent functions on $\Delta=\{z\in\mathbb{C}: |z|>1\}$, obtain their coefficient estimates. The results presented in this paper generalize the recent work S.A.Halim et al.[1].

In this paper we study the existence and the uniqueness of isoperimetric extremals of rotation on two-dimensional (pseudo-) Riemannian manifolds and on surfaces on Euclidean space. We find the new form of their equations which is easier than results by S. G. Leiko. He introduced the notion of rotary diffeomorphisms. In this paper we propose a new proof of the fundamental equations of rotary mappings.

For getting the numerical solution of the linear complementary problem (LCP), there are many methods such as the modulus-based matrix splitting iteration and the modulus-based nonsmooth Newton?s method. We proposed the Square-Newton method to solve the LCP. This method could solve LCP efficiently. We gave the theoretical analysis and numerical experiments in the paper.

In this paper, we present the concept of generalized locally convex spaces, by introducing the socalled family of vector-valued seminorms. Some extensions of classical fixed point theorems in Hausdorff complete generalized locally convex spaces are given. These results are formulated in terms of continuity and L-contractions. As applications, we study the existence and uniqueness of solutions for systems of first order differential equations with impulsive.

In this paper, we prove that a complex square matrix is weak group matrix if the m-th power of this matrix commutes with its weak group inverse, where m is an arbitrary positive integer. Firstly, some new characterizations of weak group matrices are investigated by means of core-EP decomposition. Secondly, we study new equivalent conditions of the weak group matrix by using commutator and rank equalities. Finally, the relationships between {m, k}-core EP matrices, k-EP matrices and weak group matrices are given.

In this paper, following a new interpolation approach in fixed point theory, we introduce the concepts of interpolative Hardy-Rogers-type fuzzy contraction and interpolative Reich-Rus-Ciric type fuzzy contraction in the framework of metric spaces, and we analyze the existence of fuzzy fixed points for such contractions equipped with some suitable hypotheses. A few consequences in single-valued mappings which include the conclusion of the main result of Karapinar et al. [On interpolative Hardy-Rogers type contractions. Symmetry, 2019, 11(1), 8] are obtained. On the basis that fixed point of a single-valued mapping satisfying interpolative type contractive inequality is not necessarily unique, and thereby making the notions more appropriate for fixed point theorems of multifunctions, new multivalued analogues of the fuzzy fixed point theorems presented herein are deduced as corollaries. In addition, nontrivial examples which dwell upon the generality of our results are provided. Finally, one of our results is applied to investigate solvability conditions of a Fredholm integral inclusion.

In this paper, an isomorphism between unit dual sphere, DS2, and the subset of tangent bundle of unit 2-sphere, T?M, is represented. According to E. Study mapping, a ruled surface in IR3 corresponds to each curve on DS2. Through this isomorphism, new forms of ruled surfaces called slant ruled surfaces in IR3 were introduced. Moreover, conditions for these surfaces to be slant ruled surfaces were given. Finally, a unique ?q?,?h? and ?? slant ruled surfaces in IR3 were corresponded to each striction curve of natural lift curve on T?M.

In this paper, we introduce several various classes of (?, c)-almost periodic type functions and their Stepanov generalizations. We also consider the corresponding classes of (?, c)-almost periodic type functions depending on two variables and related composition principles. We provide several illustrative examples and applications to the abstract Volterra integro-differential equations in Banach spaces.

In the case of linear operator the property P(B, k) was introduced by M.A. Kaashoek. In this paper, we characterize the essentially semi regular linear relation in terms of the property P(B, k). After that and as an application of this result we give some connection between essentially semi regular and semi regular linear relations. Further, we will give some supplementary conditions on essentially semi regular linear relation to be semi Fredholm. Then, we analyze the stability of the class of essentially semi regular linear relations under small perturbations and Riesz operators. Finally, we study some properties of the essentially semi regular spectrum of a linear relation and we establish a spectral mapping theorem.

In this paper, we first establish a Landau-Bloch type theorem for certain bounded and normalized biharmonic mappings F(z) = |z|21(z) + h(z), where 1(z) and h(z) are harmonic in the unit disk with |1(z)| ? M1, |h(z)| ? M2. In particular, our result is sharp when M1 = M2 = 1. Then, we establish several new versions of Landau-Bloch type theorems for certain normalized biharmonic mappings with the coefficients condition in place of |h(z)| ? M2 or |1(z)| ? M1, and obtain several sharp results.