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Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a "o" instead of "o" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to introduce the notion of stabilizers in L-algebras and develop stabilizer theory in L-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a CKL-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in CKL-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on L-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. [ABSTRACT FROM AUTHOR]

Ideals and filters are important notions with different meanings in the study of algebraic structures related to logical systems. In this paper we establish new connections between these concepts in residuated lattices. [ABSTRACT FROM AUTHOR]

In this paper, we study the ideal strong lacunary ward compactness of a subset of a 2-normed space and the ideal strongly lacunary ward continuity of a function on . Here a subset of is said to be ideal strong lacunary ward compact if any sequence in has an ideal strong lacunary quasi-Cauchy subsequence. Additionally, a function on is said to be ideal strong lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences; an ideal is defined to be a hereditary and additive family of subsets of . We find that a subset of with a countable Hamel basis is totally bounded if and only if it is ideal strong lacunary ward compact. [ABSTRACT FROM AUTHOR]

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters. [ABSTRACT FROM AUTHOR]

In this paper, the concept of Paradistributive Latticoid (PDL) as a generalization of a distributive lattice is introduced and investigated its properties. A set of equivalent conditions for a PDL to become a distributive lattice are given. The notions of an ideal and a filter in a PDL are introduced and studied their properties. Subdirect representation of a PDL is obtained [ABSTRACT FROM AUTHOR]

This paper aims to examine the notion of λ-ideal statistical convergence and λ-ideal statistically Cauchy sequence over non-Archimedean 2-normed spaces. Moreover, we have also studied and proven some significant properties for λ-ideal statistically Cauchy sequence in 2-normed spaces to be λ-ideal statistically Cauchy with respect to II.II∞. And also we show that, λ-ideal statistical convergence in 2-normed spaces is λ-ideal statistical pre-Cauchy in 2-normed spaces over non-Archinedean field. Through this paper, K symbolizes a complete, non-trivially valued, non-Archinedean field. [ABSTRACT FROM AUTHOR]

In this paper new notions of dimensions for ideal topological spaces are inserted, called *-quasi covering dimension and ideal quasi covering dimension. We study several of their properties and investigate their relations with types of covering dimensions like the-covering dimension and the ideal covering dimension. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an equiprime fuzzy graph of a nearring with respect to the level ideal of a fuzzy ideal. We interrelate graph theoretical properties of the graph and ideal theoretical properties of nearring. We show that the properties like vertex cut, connectedness of the graph depend on the properties of the fuzzy ideal. We define ideal symmetry of the graph and find conditions for the graph to be ideal symmetric. If the fuzzy ideal is equiprime then we show that the level set induces a fuzzy clique. We find conditions required for the level set to be the vertex cover of the graph. We find interrelation between equiprime fuzzy graph and fuzzy graph of nearring with respect to level ideal. We study properties of the graph under neaaring homomorphism. We prove that the connectedness of the graph in homomorphic image depends on properties of ideal. We obtain conditions required for homomorphic image of an equiprime fuzzy ideal to be an equiprime fuzzy ideal. [ABSTRACT FROM AUTHOR]

In this paper, a new diamond–silicon carbide ceramic composite material—Ideal—is studied and its mechanical characteristics are determined. For the first time, a comprehensive determination of Poisson's ratio, shear modulus, bulk modulus, and transverse sound velocity is carried out. Poisson's ratio is in the region of 0.008 to 0.01, which, in turn, indicates the absolutely brittle nature of the failure of the Ideal ceramic under loading. The criteria that allow evaluating different materials used for body armor are calculated. [ABSTRACT FROM AUTHOR]

As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834-2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup S an ordered hypersemigroup V having a greatest element (poe-hypersemigroup) can be constructed in such a way that there exists a pseudoideal T of S such that S is isomorphic to T. If S does not have a greatest element, then this can be regarded as the embedding of an ordered hypersemigroup in an ordered semigroup with greatest element. [ABSTRACT FROM AUTHOR]

This is from Birkhoff, the "father of lattice theory" in Trends in Lattice Theory. Van Nostrand 1970: "Lattices can do things for you, no matter what kind of mathematician you are!". The aim of this paper is to show that the le-semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of "order" makes it easier to investigate the lattice ordered semigroup at first. After getting the results on ordered semigroups, by an easy modification corresponding results on ordered hypersemigroups can be obtained. [ABSTRACT FROM AUTHOR]

BL-algebras are algebraic structures corresponding to Hajek's basic fuzzy logic. The aim of this paper is to analyze the structure of BL-algebras using commutative rings. Due to computational considerations, we are interested in the finite case. We present new ways to generate finite BL-algebras using commutative rings and provide summarizing statistics. Furthermore, we investigated BL-rings, i.e., commutative rings whose the lattice of ideals can be equipped with a structure of BL-algebra. A new characterization for these rings and their connections to other classes of rings is established. Furthermore, we give examples of finite BL-rings for which the lattice of ideals is not an MV-algebra and, using these rings, we construct BL-algebras with 2 r + 1 elements, r ≥ 2 , and BL-chains with k elements, k ≥ 4. In addition, we provide an explicit construction of isomorphism classes of BL-algebras of small n size ( 2 ≤ n ≤ 5 ). [ABSTRACT FROM AUTHOR]

It is shown that some embedding problems on hypersemigroups are actually problems of adjunction. According to the theorem of this paper, for every hypersemigroup S which does not have identity element, an hypersemigroup T having identity element can be constructed in such a way that S is an ideal of T. Moreover, if S is regular, intra-regular, right (left) regular, right (left) quasi-regular or semisimple, then so is T. If A is an ideal, subidempotent bi-ideal or quasi-ideal of S, then it is an ideal, bi-ideal, quasi-ideal of T as well. Illustrative examples are given. [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the notion of rough I-convergence in intuitionistic fuzzy normed spaces. Also we have defined rough I-cluster point of a sequence and proved some related results in the same space. [ABSTRACT FROM AUTHOR]

In this paper, we characterize residuated lattices for which the topological space of prime ideals is a Noetherian space. The notion of i-Noetherian residuated lattice is introduced and related properties are investigated. We proved that a residuated lattice is i-Noetherian iff every ideal is principal. Moreover, we show that a residuated lattice has the spectrum of a Noetherian space iff it is i-Noetherian. [ABSTRACT FROM AUTHOR]

The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object's symmetries. In this paper, we introduce new concepts in an algebraic structure called BCI-algebra, where we present the concepts of bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy (closed) BCI-commutative ideals of BCI-algebras. The relationship between bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy ideals is investigated, and various conditions are provided for a bipolar fuzzy ideal to be a bipolar fuzzy BCI-positive implicative ideal. Furthermore, conditions are presented for a bipolar fuzzy (closed) ideal to be a bipolar fuzzy BCI-commutative ideal. [ABSTRACT FROM AUTHOR]

We give a counterexample in this amendment to show that there is an error in consideration of the statement "if f: X → Y and J is an ideal on Y, then f-1(J) = ff-1(J): J ℇ J- is an ideal on X" by Hamlett in his paper "Lindelöf with respect to an ideal" [New Zealand J. Math. 42, 115-120, 2012]. We also modify it here in a new way and henceforth put forward correctly all the results that were based on the said statement derived therein. [ABSTRACT FROM AUTHOR]

The structure theorems for (Completely) simple semigroups and (Completely) 0-simple semigroups have proved a powerful tool in the investigation of such semigroups. In this paper, first of all, we define weak simple semigroups and weak 0-simple semigroups and compare them with simple semigroups and 0-simple semigroups respectively. Then we give examples of these semigroups and describe the structure of them. Also, we define completely weak simple semigroup and completely weak 0-simple semigroup. Finally, by using Green's equivalences, we prove some results and give equivalences, for these semigroups. [ABSTRACT FROM AUTHOR]

The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, in particular, we pay attention to their characterizations based on of the lattice min and max operations. In addition, we study the notion of prime single-valued neutrosophic ideal (respectively, filter) as interesting kind and we discuss some its set-operations, complement and associate sets. [ABSTRACT FROM AUTHOR]

Let T(X) be the full transformation semigroup on the set X . For a fixed nonempty subset Y of X, let PGY (X) = {α ∈ T(X) : α|Y ∈ G(Y )} where G(Y ) is the permutation group on Y . It is known that P GY (X) is a regular subsemigroup of T(X). In this paper, we give a simpler description of Green’s relations and characterize the ideals of P GY (X). Moreover, we prove some isomorphism theorems for PGY (X). For finite sets, we investigate the cardinalities of PGY (X) and of its subsets of idempotents, and we also calculate their ranks. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concepts of para and quasi topological MV -algebras, which was first introduced by Najafi et al. in 2017, to BL-algebras as para and quasi topological BL-algebras and elaborate these concepts via some examples. We further derive and prove some theorems by employing pre-filters and a fundamental system of neighborhoods. [ABSTRACT FROM AUTHOR]

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F : X → E restricted to [c, F(c)]? is partially ideal statistically continuous at c then E is singleton. [ABSTRACT FROM AUTHOR]

In this paper we mainly deal with I(q) c -convergence. In particular we study bounded multipliers of bounded I(q) c -convergent sequences. We also give some I-core results and characterize the inclusion K-core {Ax} ⊆ I-core {x} for bounded sequences x = (xn). [ABSTRACT FROM AUTHOR]

In this paper we study Morita contexts between rings without identity. We prove that if two associative rings are connected by a Morita context with surjective mappings, then these rings have isomorphic quantales of unitary ideals. We also show that the quotient rings by ideals that correspond to each other under that isomorphism are connected by a Morita context with surjective mappings. In addition, we consider how annihilators and two-sided socles behave under that isomorphism. [ABSTRACT FROM AUTHOR]

This paper is devoted to studies of I wQN-spaces and some of their cardinal characteristics. Recently, Šupina in [32] proved that I is not a weak P-ideal if and only if any topological space is an I QN-space. Moreover, under p = c he constructed a maximal ideal I (which is not a weak P-ideal) for which the notions of I QN-space and QN-space do not coincide. In this paper we show that, consistently, there is an ideal I (which is not a weak P-ideal) for which the notions of I wQN-space and wQN-space do not coincide. This is a partial solution to [6, Problem 3.7] . We also prove that for this ideal the ideal version of Scheepers Conjecture does not hold (this is the first known example of such weak P-ideal). We obtain a strictly combinatorial characterization of non ( I wQN-space ) similar to the one given in [32] by Šupina in the case of non ( I QN-space ) . We calculate non ( I QN-space ) and non ( I wQN-space ) for some weak P-ideals. Namely, we show that b ≤ non ( I QN-space ) ≤ non ( I wQN-space ) ≤ d for every weak P-ideal I and that non ( I QN-space ) = non ( I wQN-space ) = b for every F σ ideal I as well as for every analytic P-ideal I generated by an unbounded submeasure (this establishes some new bounds for b ( I , I , Fin ) introduced in [31] ). As a consequence, we obtain some bounds for add ( I QN-space ) . In particular, we get add ( I QN-space ) = b for analytic P-ideals I generated by unbounded submeasures. By a result of Bukovský, Das and Šupina from [6] it is known that in the case of tall ideals I the notions of I QN-space ( I wQN-space) and QN-space (wQN-space) cannot be distinguished. Answering [6, Problem 3.2] , we prove that if I is a tall ideal and X is a topological space of cardinality less than co v ⁎ ( I ) , then X is an I wQN-space if and only if it is a wQN-space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of neutrosophic ℵ-bi-ideal for a semigroup. We infer different semigroups using neutrosophic ℵ -bi-ideal structures. Moreover, for regular semigroups, neutrosophic ℵ-product and intersection of neutrosophic ℵ-ideals are identical. [ABSTRACT FROM AUTHOR]

As we have already seen in Turkish Journal of Mathematics (2019) 43: 2592--2601 many results on hypersemigroups do not need any proof as they can be obtained from lattice ordered semigroups. The present paper goes a step further, to show that many results on Γ-hypersemigroups as well can be obtained from lattice ordered semigroups. It can be instructive to prove them directly, but even in that case the proofs go along the lines of lattice ordered semigroups (or poe-semigroups). In the investigation, we faced the problem to correct the definition of Γ-hypersemigroups given in the existing bibliography. [ABSTRACT FROM AUTHOR]

As pointed out in the monographs [5, 6] on semirings, ideals play an important role despite the fact that they need not be congruence kernels as in the case of rings. Hence, having two commutative semirings S1 and S2, one can ask whether an ideal I of their direct product S = S1 ×S2 can be expressed in the form I1 ×I2 where Ij is an ideal of Sj for j = 1,2. Of course, the converse is elementary, namely if Ij is an ideal of Sj for j = 1,2 then I1 × I2 is an ideal of S1 × S2. Having a congruence Θ on a commutative semiring S, its 0-class is an ideal of S, but not every ideal is of this form. Hence, the lattice IdS of all ideals of S and the lattice KerS of all congruence kernels (i.e. 0-classes of congruences) of S need not be equal. Furthermore, we show that the mapping Θ 7→ [0]Θ need not be a homomorphism from ConS onto KerS. Moreover, the question arises when a congruence kernel of the direct product S1 ×S2 of two commutative semirings can be expressed as a direct product of the corresponding kernels on the factors. In the paper we present necessary and sufficient conditions for such direct decompositions both for ideals and for congruence kernels of commutative semirings. We also provide sufficient conditions for varieties of commutative semirings to have directly decomposable kernels. [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of AI-statistical convergence for real sequences and establish a Korovkin type approximation theorem for positive linear operators on UC*[0;1), the Banach space of all real valued uniform continuous functions on [0;∞) with the property that limx!∞ f(x) exists finitely for any f 2 UC*[0;∞). We then construct an example which shows that our new result is stronger than its classical version. In the section 3, we extend the Korovkin type approximation theorem for positive linear operators on UC*([0;∞) × [0;∞)). [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of I-equal convergence introduced by Das, Dutta, and Pal [9], and two related notions of convergence, namely, I-discrete, and I -strong uniform equal convergence and primarily investigate some lattice properties of the corresponding Baire classes obtained from a class of functions $. [ABSTRACT FROM AUTHOR]

In this paper we have introduced two new types of sets termed as I* -open sets and strongly I* -open sets and discussed some of its properties. The relation between similar types of sets, characterizations and some basic properties of such sets have been studied. [ABSTRACT FROM AUTHOR]

New approaches in topology or related branches of mathematics have contributed in a valuable way to the science, and have yielded various new topics for investigation. The main goal of this paper is to examine a new approach and so a new form of open sets via elements of an ideal. The concept of α*I-open sets is introduced and discussed. [ABSTRACT FROM AUTHOR]

Abstract In this paper we primarily introduce certain new versions of groupability, namely star- I -groupability which is introduced using both star operation and the notion of ideals and then a more general notion of R -groupability. We establish several results regarding these groupability notions in the process of extending certain existing results on groupability. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [6] (where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of weight g and I-lacunary statistical convergence of weight g, where g : N → [0;∞) is a function satisfying g (n) → ∞ and n/g (n) → 0. We mainly investigate their relationship and also make some observations about these classes. Our results extend the recent results of [7]. [ABSTRACT FROM AUTHOR]

Fuzzy sets, formalized by Zadeh in 1965, generalizes the classical idea of sets. The idea itself was generalized in 1975 when Zadeh introduced the interval-valued fuzzy sets. In this paper, we generalize further the above concepts by introducing interval-valued fuzzy on ideal sets, where an ideal is a nonempty collection of sets with a property describing the notion of smallness. We develop its basic concepts and properties and consider how one can create mappings of interval-valued fuzzy on ideal sets from mappings of ordinary sets. We then consider topology and continuity with respect to these sets. [ABSTRACT FROM AUTHOR]

In this paper, we introduce β-paracompactness with respect to an ideal (I-β-paracompactness) as a weak form of β-paracompactness and I-paracompactness. We give some relations between this concept and some other types of paracompactness, and also we study some of its fundamental properties. [ABSTRACT FROM AUTHOR]

This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-I-set) which is a pragmatic approach to characterize completely Hausdorff spaces. [ABSTRACT FROM AUTHOR]

The notion of β1-paracompactness in topological spaces is introduced and studied in [1]. In this paper, we introduce and investigate the notion of β1-paracompact spaces with respect to an ideal I which is a generalization of the notion of β1-paracompact spaces. We study characterizations, subsets and subspaces of β1I-paracompact spaces. Also, we investigate the invariants of β1I-paracompact spaces by functions. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of n-fold implicative ideals and n-fold obstinate ideals in BL-algebras are introduced. With respect to this concepts, some related results are given. In particular, it is proved that an ideal is an n-fold implicative ideal if and only if is an n-fold Boolean ideal. Also, it is shown that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal {0} is an n-fold obstinate ideal. Moreover, the relation between n-fold obstinate ideals and n-fold (integral) obstinate filters in BL-algebras are studied by using the set of complement elements. Finally, it is proved that ideal I of BL-algebra L is an n-fold obstinate ideal if and only if L/I is an n-fold obstinate BL-algebra. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study triple difference sequence spaces over n-normed space via the sequence of modulus functions. Some algebraic and topological properties of the newly constructed spaces are also established. [ABSTRACT FROM AUTHOR]

We consider four classes of topological spaces which are defined with the aid of convergence with respect to ideals on N . All these classes are subclasses of countably compact spaces, and two of them are also subclasses of sequentially compact spaces. In the first part of the paper (Sections 1 and 2 ) we prove some properties of these classes. In the second part of the paper (Sections 3 and 4 ) we focus on spaces defined by two particular ideals connected with well known theorems in combinatorics, namely van der Waerden's theorem and Hindman's theorem. The main aim of this part of the paper is to show that two classes of the considered spaces coincide for the van der Waerden ideal and Hindman ideal respectively. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring. A mapping F: R → R (not necessarily additive) is called a multiplicative (generalized) reverse derivation if there exists a map d: R → R (not necessarily a derivation nor an additive map) such that F(xy) = F(y)x + yd(x) for all x; y 2 R. In this paper we investigate some identities involving multiplicative (generalized) reverse derivation and prove some theorems in which we characterize these mappings. [ABSTRACT FROM AUTHOR]

In this paper we primarily consider the ideal analogue of Hurewicz property introduced recently by Das in [6] and subsequently introduce the ideal analogues of several versions of this very important property studied in the last decade. We establish certain inter relationships between the new notions presenting suitable examples as far as possible as well as prove many related results and in particular preservation properties. [ABSTRACT FROM AUTHOR]

The sequence space 𝐵BVσ was introduced and studied by Mursaleen [Houston J. Math. 9, 505-509 (1983; Zbl 0542.40003)]. The main aim of this paper is to study some new double sequence spaces of invariant means defined by ideal and modulus function. Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In order to accurately, robustly and efficiently simulate the three-dimensional (3D) interfacial flow problems with large density and viscosity ratio, we should, on the one hand, adopt the accurate and robust interface capturing method, on the other hand, use the efficient solution algorithm for coupling the velocity and pressure. In this paper, a coupled volume-of-fluid and level set (VOSET) method is applied to capture the two-phase interface, while an inner doubly iterative efficient algorithm for linked equations (IDEAL) is used to couple the velocity and pressure. Both of the VOSET method and the IDEAL algorithm were first proposed by the present author and further extended by other authors. Finally, the superiority of the VOSET method combined with the IDEAL algorithm (VOSET + IDEAL) is verified by three interfacial flow problems with large density and viscosity ratio. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of generalized terminal sections in BE-algebras and investigate their properties. Furthermore, these sets are considered in commutative and self distributive BE-algebras. Finally, we provide the relationship between self distributive and ideal and the relationship between self distributive and filter. [ABSTRACT FROM AUTHOR]

• Numerical performances of IDEAL and SIMPLERR are analyzed and compared. • SIMPLERR can be regarded as a special form of IDEAL. • The robustness of IDEAL is much better than SIMPLERR. • In general, the performance of IDEAL is superior to SIMPLERR. In this paper, the numerical performances of the algorithm IDEAL proposed by the present authors in 2008, and the recently proposed (2017) SIMPLERR are systematically analyzed and compared via six incompressible fluid flow and heat transfer problems. It is found that the two algorithms are almost identical when the second inner iteration number of IDEAL is fixed at 2. In general, the robustness and convergence of IDEAL are much better than SIMPLERR. The reason why the performance of SIMPLERR deteriorates with the increase of the first inner iteration number is analyzed and detailed comparisons in the robustness and computing time are presented. [ABSTRACT FROM AUTHOR]

In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties of neutrosophic LA-semigroup in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we continue our investigations in line of our recent papers, Savas and Das [16] and Das, Savas and Ghosal [5]. We introduce the notion of AI-statistical convergence which includes the new summability methods studied in [16] and [5] as special cases and make certain observations on this new and more general summability method. [ABSTRACT FROM AUTHOR]