(strongly) b

The trapezoidal-type inequalities are discovered in this study using the fractional operator, which produces powerful results. We established a general identity for Caputo-Fabrizio integral operators and the second derivative function. Using this identity new error bounds and estimates for strongly $(s,m)$-convex functions are obtained. Moreover, some noveltrapezoidal-type inequalities are offered taking this identity into account using the known inequalities like Young, Jensen, H\"{o}lder and power-mean inequalities. Finally, we present some applications for matrix inequality, estimation error regarding trapezoidal formulas and special means for real numbers.

‎The purpose of this paper is to extend the mixture factor analyzers (MFA) model \CG{to handle} missing and heavy-\CG{tailed} data‎. ‎In this model‎, ‎the distribution of factors loading and errors arise from the multivariate normal mean-variance mixture of‎ \CG{the} Birnbaum-Saunders (NMVBS) distribution‎. ‎By using the structures covariance matrix‎, ‎we introduce parsimonious MFA based on NMVBS distribution‎. ‎An Expectation Maximization (EM)-type algorithm is developed for parameter estimation‎. ‎Simulations study and real data sets represent the efficiency and performance of the proposed model‎.

The notion and some properties of (strongly) B-rings, in a natural way, are extended to (strongly) B- and (strongly) BJ-semirings which is somewhat similar to the notion of rings having stable range 2. Results are given showing the connection between several types of semirings whose finite sequences satisfy some stability condition, some involving the Jacobson k-radical of the semiring R. Besides some examples and other results, it is shown that R[x], the semiring of polynomials over a semiring R, is not a B-semiring (consequently, not a strongly B-semiring) when R is a zerosumfree semiring. We also study some algebraic properties of the S-relative B- and BJ-semirings with respect to a nonempty subset S of R.

In the current study, a one-step numerical algorithm is presented to solve strongly non-linear full fractional duffing equations. A new fractional-order operational matrix of integration via  quasi-hat functions (QHFs) is introduced. Utilizing the operational matrices of QHFs, the main problem will be transformed into  a number of univariate polynomial equations. Absolute errors of the results in approximations and convergence analysis are addressed. Ultimately, five examples are provided to illustrate the capabilities of this algorithm. The numerical results are illustrated in some Tables and Figures, for different values of the parameters $\alpha~ and~ \beta$.

For a non-zero normed linear space $A$, we consider $ C^b\left(K\right) $, the complex-valued, bounded and continuous functions space on $K$ with $ \left\| \cdot \right\|_\infty $, where $ K = \overline{B^{\left(0\right)}_1} $ (the closed unit ball of $A$). Also for a non-zero element $\varphi \in A^*$ with $ \left\| \varphi \right\| \leq 1 $, we consider the space $ C^{b\varphi}\left(K\right) $ as the linear space $ C^b\left(K\right) $ with the new norm $ \left\| f \right\|_\varphi = \left\| f\varphi \right\|_\infty $ for all $ f \in C^b\left(K\right) $. Some basic properties such as, proximinality, E-proximinality, strongly proximinality and quasi Chebyshev for certain subsets of $ C^b\left(K\right) $ are characterized with the norms $ \left\| \cdot \right\|_\varphi $ and $ \left\|\cdot \right\|_\infty $. Some examples for illustration and for comparison between the norms $ \left\| \cdot \right\|_\varphi $ and $ \left\| \cdot \right\|_\infty $ on $ C^b\left(K\right) $ are presented.

The notions of a prime (strongly prime, semiprime, irreducible, and strongly irreducible) double-framed soft bi-ideals (briefly, prime, (strongly prime, semiprime, irreducible and strongly irreducible) DFS bi-ideals) in ordered semigroups are introduced and related properties are investigated. Several examples of these notions are provided. The relationship between prime and strongly prime, irreducible and strongly irreducible DFS bi-ideals are considered and  haracterizations of these concepts are established. The Characterizations of regular and intraregular ordered semigroups in terms of these notions are studied.

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of N. In addition, they obtained the relation between strongly prime ideal and strongly prime N-group, and also between Pseudo-valuation near ring and Pseudo-valuation N-subgroup. It has also shown that if every N-subgroup be ideal of M and P be a strongly prime N-subgroup of M, then (P: M) is a strongly prime ideal of N. And in the end it is proved that if P‎‎ and L of ‎N-subgroups M‎ and Psubset of L ‎such ‎that ‎for ‎any‎ y in K ‎,y-1P subset of P , then L is a strongly prime N-subgroup of M if and only if L/p ‎is a ‎strongly ‎prime ‎N-subgroup ‎of‎ M/p .

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of a strongly zero-product, strongly Jordan zero-product and strongly Lie zero-product preserving map on a certain class of normed algebras are investigated.

In this paper, we consider double sequence iteration processes for strongly $rho$-contractive mapping in modular space. It is proved, these sequences, convergence strongly to a fixed point of the strongly $rho$-contractive mapping.

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule C, C--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which admit minimal resolutions of C--projective modules.

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) R-module is T-dual Rickart if and only if overlineZ2(R) is a direct summand of R and End(overlineZ2(R)) is a semisimple (resp. regular) ring. It is shown that, while a direct summand of a (strongly) T-dual Rickart module inherits the property, direct sums of T-dual Rickart modules do not. Moreover, when a direct sum of T-dual Rickart modules is T-dual Rickart, is included. Examples illustrating the results are presented.

Abstract. In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct product and the composition of two strongly Jordan zero-product preserving maps are again strongly Jordan zero-product preserving maps. But this fact is not the case for tensor product of them in general. Finally, we prove that every ∗−preserving linear map from a normed∗−algebra into a C∗−algebra that strongly preserves Jordan zero-products is necessarily continuous.

A subgroup H of a group G is called inert if, for each g∈G, the index of H∩H g in H is finite. We give a classification of soluble-by-finite groups G in which subnormal subgroups are inert in the cases where G has no nontrivial torsion normal subgroups or G is finitely generated.

The main result of this paper gives a characterization of association schemes having commutative thin thin residue. This gives a generalization of Ito's Theorem on finite groups for association schemes.

A new approximation method for the set of common fixed points of nonexpansive mappings and the set of solutions of systems of variational inequalities is introduced and studied. Moreover, we apply our main result to obtain strong convergence theorem to a common fixed point of a nonexpannsive mapping and solutions of a system of variational inequalities of an inverse strongly monotone mapping and strictly pseudo-contractive mapping of Browder-Petryshyn type.

A ring $R$ is a strongly clean ring if every element in $R$ is the sum of an idempotent and a unit that commutate. We construct some classes of strongly clean rings which have stable range one. It is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

n this paper, we propose a generalized iterative method for finding a common element of the set of fixed points of a single nonexpannsive mapping and the set of solutions of two variational inequalities with inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mapping. Our results improve and extend the results announced by many others.

Two new topologies are defined on C(X). These topologies makeC(X) to be a zero-dimensional (completely regular) Hausdorff space.C(X) endowed by these topologies is denoted by Co(X) andCo−1 (X). The relations between X, Co(X) and Co−1 (X) are studied and closedness of z-ideals and maximal ideals are investigated in Co(X)and Co−1 (X).