Journal of Mathematical Extension
Volume:16 Issue: 6, Jun 2022

The aim of this research is to define ⊥-proximally increasing mapping and obtain several best proximity point results concerning this mapping in the framework of new spaces, which is called orthogonal bmetric spaces. Also, several well-known fixed point results in such spaces are established. All main results and new definitions are supported by some illustrative and interesting examples.

The aim of this paper is to introduce the notion of pseudo CI-filter in the pseudo CI-algebra and defined of congruence relation, transitive CI-algebra and pseudo CI-filters generated by a set. The Maximal pseudo-filter, prime pseudo CI-filter and closed pseudo CIfilter are defined, and we show that each Maximal pseudo CI-filter is a prime pseudo CI-filter. With an example, it shows that the inverse is not true. Define of homomorphism on CI-algebras is another aim of this article, and proves that every homomorphic image and preimage of a pseudo CI-filter is also a pseudo CI-filter. Furthermore, there are some relations between prime pseudo CI-filters, Maximal pseudo CI-filters and generated pseudo CI-filters. The notion of congruence relations on pseudo CI-algebras is one of the purposes of this article. There are some relations between pseudo CI-filters and pseudo congruence. Also, the transitive CI-algebra and generated pseudo CI-filter are introduced.

Fuzzy fractional heat equations (FFHEs) are utilized to analyze the behaviour of the certain phenomena in various mathematical and scientific models. The main goal of this paper is to construct the solution of fuzzy fractional heat equations by taking a reliable recipe of Sumudu transformation method and homotopy analysis method into account. These method allow us to remove the difficulties and restrictions confronted in other methods. The feasibility of this method is confirmed by given numerical examples. The result presented that the proposed method is suitable, powerful and reliable for obtaining the solution of fuzzy fractional problems with FFHEs.

In this paper introduced the notion of a strong synchronized system; that is a synchronized system whose there is unique finite path in Fischer cover labeled synchronizing block. We aim to introduce a class of synchronized systems containing sofics. Every irreducible sofic shift is an strong synchronized.

In this study we continue an investigation of the notion of module approximate amenability of a Banach algebra A which is a module over another Banach algebra A. In fact we introduce the class of module boundedly approximately amenable Banach algebras (m.b.app.am.) . It is shown that the class of module boundedly approximately amenable Banach algebra is different from the class of amenable Banach algebras. Also, we show that for an inverse semigroup S with the set of idempotent E, l 1 (S) is module boundedly approximately amenable as l 1 (E)-module if and only if S is amenable. Further examples are given of l 1 -semigroup Banach algebras which are module boundedly approximately amenable but are not amenable.

We study a family of harmonic univalent functions using an operator involving q–derivative and hypergeometric functions. We then obtain necessary and sufficient condition bounds for functions in this family. Extreme points and convex set for such functions are also introduced.

The paper deals with the notion of quasi bi-slant submersions from almost contact metric manifolds onto Riemannian manifolds. These submersions are generalization of hemi-slant submersions and semi-slant submersions. We study such submersions from Kenmotsu manifolds onto Riemannian manifolds and discuss some examples of it. In this paper, we also study the geometry of leaves of distributions which are involved in the definition of the submersion. Further, we obtain the conditions for such submersions to be integrable and totally geodesic.

The perfect m-coloring with matrix A = [aij ]i,j∈{1,··· ,m} of a graph G = (V, E) with {1, · · · , m} color is a vertex coloring of G with m-color so that the number of vertices in color j adjacent to a fixed vertex in color i is aij , independent of the choice of vertex in color i. The matrix A = [aij ]i,j∈{1,··· ,m} is called the parameter matrix. We study the perfect 4-colorings of the 3-regular graphs of order at most 8, that is, we determine a list of all color parameter matrices corresponding to perfect 4-colorings of 3-regular graphs of orders 4, 6, and 8.

We give formulas for the number of fuzzy subgroups of all small p-groups of order at most p 4 as polynomials in prime p.

The power version of the modified Lindley distribution is introduced in this paper, offering a new two-parameter lifetime distribution. As a main interest, it provides a motivated alternative to the Weibull and power Lindley distributions. We discuss its main characteristics and properties, including shapes of the probability density and hazard rate functions, incomplete moments, crude moments, variance, skewness, kurtosis and order statistics. Then, a statistical study of the model is developed. The parameters are estimated by the maximum likelihood method. A simulation study examines the numerical comportment of the bias and mean square error of the maximum likelihood estimates of the parameters. Application of the new model to three data sets is presented, showing that the model has a better fit behavior in comparison to some other well-known lifetime models, including the Weibull and power Lindley models.