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The object of the present paper is to study the notion of quasi-bi-slant submanifolds of almost contact metric manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant, and quasi-hemi-slant submanifolds. We study and characterize quasi-bi-slant submanifolds of Sasakian manifolds and provide non-trivial examples to signify that the structure presented in this paper is valid. Furthermore, the integrability of distributions and geometry of foliations are researched. Moreover, we characterize quasi-bi-slant submanifolds with parallel canonical structures.

In this paper, we introduce a cyclic subgradient extragradient algorithm and its modified form for finding a solution of a system of equilibrium problems for a class of pseudomonotone and Lipschitz-type continuous bifunctions. The main idea of these algorithms originates from several previously known results for variational inequalities. The proposed algorithms are extensions of the subgradient extragradient method for variational inequalities to equilibrium problems and the hybrid (outer approximation) method. The paper can help in the design and analysis of practical algorithms and gives us a generalization of the most convex feasibility problems.

In this paper, we study a system of nonlinear Riemann–Liouville fractional differential equations with delays. First, we define in an appropriate way initial conditions which are deeply connected with the fractional derivative used. We introduce an appropriate generalization of practical stability which we call practical stability in time. Several sufficient conditions for practical stability in time are obtained using Lyapunov functions and the modified Razumikhin technique. Two types of derivatives of Lyapunov functions are used. Some examples are given to illustrate the introduced definitions and results.

Ateş, Fırat (Balikesir Author), For arbitrary monoidsAandB, in Cevik et al. (Hacet J Math Stat 2019:1-11, 2019), it has been recently defined an extended version of the general product under the name ofa higher version of Zappa products for monoids(orgeneralized general product)A(circle plus B) (delta)(sic)(psi) B-circle plus A and has been introduced an implicit presentation as well as some theories in terms of finite and infinite cases for this product. The goals of this paper are to present some algebraic structures such as regularity, inverse property, Green's relations over this new generalization, and to investigate some other properties and the product obtained by a left restriction semigroup and a semilattice., Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah G:1709-247-1440

Let R a commutative ring with identity and M be a unitary R-module. In this paper, we investigate some properties of n-absorbing submodules of M as a generalization of 2-absorbing submodules. We also define the classical n-absorbing submodule, a proper submodule N of an R-module M is called a classical n-absorbing submodule if whenever $$a_1 a_2\ldots a_{n+1} m\in N$$ a 1 a 2 … a n + 1 m ∈ N for $$a_1, a_2,\ldots , a_{n+1}\in R$$ a 1 , a 2 , … , a n + 1 ∈ R and $$m \in M$$ m ∈ M , there are n of $$a_i$$ a i ’s whose product with m is in N. Furthermore, we give some characterizations of n-absorbing and classical n-absorbing submodules under some conditions.

In this paper, we first obtain a generalized integral identity for twice local fractional differentiable mappings on fractal sets $${\mathbb {R}}^{\alpha }\, (0

We introduce two generalizations, the first of which generalizes the concept of multiresolution analysis. We define the irregular generalized multiresolution analysis (IGMRA). This structure is defined taking translations on sets that are not necessarily regular lattices, for which certain density requirements are required, and without using dilations, also allows each subspace of IGMRA to be generated by outer frames of translations of different functions. The second generalization concerns the concept of association of wavelets to these new structures. We take frames of translations of a countable set of functions, which we called generalized wavelets, and define the concept of association of these generalized wavelets to those previously defined IGMRA. In the next stage, we prove two existence theorems. In the first theorem, we prove existence of IGMRA, and in the second existence of generalized wavelets associated with it. In the latter, we show that we are able to associate frames of translations with optimal localization properties, to IGMRA. In the last section of this paper, concrete examples of these structures are presented for L 2 ( R ) and for L 2 ( R 2 ) .