Annals of Communications in Mathematics

AbstractIn this work, we investigate the existence of solutions for Hadamard fractional differential equations with integral boundary conditions in a Banach space. We will make use the measure of noncompactness and the Monch fixed point theorem to prove the ¨ main results. An example is given to illustrate our results.

AbstractThe concept of meet-commutative UP-algebras was introduced in 2016 by Sawika et al. Muhiuddin et al. introduced in 2021 the concept of prime UP-filter (of the first kind) and irreducible UP-filter in meet-commutative UP-algebras. Also, it has been shown that any prime UP-filter in such algebras is irreducible. In this paper, we introduce the concept of weakly irreducible UP-filters in such algebras and show that the prime UPfilter is between this and the irreducible UP-filter. Also, we show the possibility that each irreducible UP-filter is a weakly irreducible UP-filter

AbstractIn this paper, we study various almost ideals (shortly A -ideals), quasi A – ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in semiring and give some characterizations. Some relevant counter examples are also indicated. We develop the implications ideal =⇒ quasi ideal =⇒ bi quasi ideal =⇒ tri quasi ideal =⇒ tri quasi A -ideal =⇒ bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in semiring.

AbstractIn this paper the concept of types of intuitionistic fuzzy e ?-connected and intuitionistic fuzzy e ?-extremally disconnected in intuitionistic fuzzy topological spaces are introduced and studied. Here we introduce the concepts of intuitionistic fuzzy e ?C5- connectedness, intuitionistic fuzzy e ?CS-connectedness, intuitionistic fuzzy e ?CM-connectedness, intuitionistic fuzzy e ?-strongly connectedness, intuitionistic fuzzy e ?-super connectedness, intuitionistic fuzzy e ?Ci-connectedness (i = 1, 2, 3, 4), and obtain several properties and some characterizations concerning connectedness in these spaces.

AbstractIn this paper we introduce the concept of interval-valued Pythagorean fuzzy subsemihypergroup and interval-valued Pythagorean fuzzy weak bi-hyperideals in hypersemigroups. We show that the (˜α, β˜)−level set of interval-valued Pythagorean fuzzy weak bi-hyperideal is a weak bi-hyperideal in hypersemigroup. We characterize cartesian product of interval-valued Pythagorean fuzzy set and examine that the cartesian product of interval-valued Pythagorean fuzzy weak bi-hyperideals is also an interval-valued Pythagorean weak bi-hyperideal in hypersemigroups.

AbstractThe purpose of this paper is to introduce the notion of soft regular semi compactness, connectedness, and separation axioms using regular semiopen soft sets in soft topological spaces. Moreover, we investigate soft RS-regular space and soft RSnormal space are soft to pological properties under bijection, soft regular semi irresolute and soft regular semi irresolute open functions. Also, we show that the properties of being soft regular semi Ti-spaces (i = 1, 2, 3, 4) are hereditary properties.

AbstractWe discuss the notion of Pythagorean subbisemiring, level sets of Pythagorean subbisemirings and Pythagorean normal subbisemiring of a bisemiring. Also, we investigate some of the properties related to subbisemirings. The fuzzy subset L = (πPL , ωPL ) is a Pythagorean subbisemiring if and only if all non-empty level set L(t,s) (t, s ∈ (0, 1]) is a subbisemiring. The cartesian product of two Pythagorean subbisemiring is also Pythagorean subbisemiring. The homomorphic image and preimage of Pythagorean subbisemiring is also Pythagorean subbisemiring. To illustrate our results and examples are given.

AbstractIn the present paper, we introduce the relative left, right, lateral, two-sided hyperideal, relative quasi-hyperideal, relative bi-hyperideal, relative sub-idempotent ordered bi-hyperideal, relative generalized quasi-hyperideal, relative generalized bi-hyperideal, relative regularity of ordered ternary semihypergroups and relative left (right, lateral) simple ordered ternary semihypergroups. We characterize relative regular ordered ternary semihypergroups through relative quasi-hyperideals and relative bi-hyperideals. We also obtain some results based on relative simple ordered ternary semihypergroups, and other results connecting these relative hyperideal-theoretic notions.