Purpose The purpose of this paper is to investigate the commutativity of quotient near-rings endowed with a left derivation and a multiplier satisfying specific differential algebraic identities, and to clarify the role of the 3-prime condition in this context. Design/methodology/approach The study considers a right near-ring N together with a 3-prime ideal P and a nonzero semigroup ideal I⊈P, and defines induced structures on the quotient near-ring N/P. Known results on derivations, left derivations and multipliers on near-rings are combined with several new lemmas to derive sufficient conditions that ensure N/P becomes a commutative ring. Findings The main results show, in particular, that if a non-P-trivial left derivation and a suitable multiplier on N satisfy certain differential identities on I, then the quotient near-ring N/P is necessarily commutative. The paper also establishes that, under the imposed hypotheses, there is no non-P-trivial left derivation on N, emphasizing the strength of the structural assumptions. Originality/value This work extends existing commutativity criteria for prime and semiprime near-rings by focusing on quotient near-rings equipped simultaneously with left derivations and multipliers that obey new differential identities. By restricting the analysis to suitable ideals of N, the paper highlights new mechanisms through which derivations and multipliers enforce commutativity in quotient near-ring structures.

PurposeThis paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.Design/methodology/approachThis paper considered theoretical and numerical methodologies.FindingsThis paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.Originality/valueThe novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

PurposeThis study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).Design/methodology/approachThe authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions.FindingsThe authors find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1).Originality/valueThis paper is an original research idea. It will be a main reference for many applications such as solving partial differential equations. If so(3,1) is part of the symmetry Lie algebra, then the subalgebras listed in this paper will be used to reduce the order of the partial differential equation (PDE) and produce non-equivalent solutions.

PurposeLet b¯2,3(n), which enumerates the number of (2, 3)-regular overcubic bipartition of n. The purpose of the paper is to describe some congruences modulo 8 for b¯2,3(n). For example, for each α ≥ 0 and n ≥ 1, b¯2,3(8n+5)≡0(mod8), b¯2,3(2⋅3α+3n+4⋅3α+2)≡0(mod8).Design/methodology/approachH.C. Chan has studied the congruence properties of cubic partition function a(n), which is defined by ∑n=0∞a(n)qn=1(q;q)∞(q2;q2)∞.FindingsTo establish several congruence modulo 8 for b¯2,3(n), here the author keeps to the classical spirit of q-series techniques in the proofs.Originality/valueThe results established in the work are extension to those proved in ℓ-regular cubic partition pairs.

PurposeBi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented.Design/methodology/approachSome properties of Di-geodesic and Di-umbilical bi-slant submanifolds are examined.FindingsThe Riemannian curvature invariants of these submanifolds are computed, and some results are discussed with the help of these invariants.Originality/valueThe topic is original, and the manuscript has not been submitted to any other journal.

PurposeThe authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions WQ on X0(N) for N ≤ 50 are Weierstrass points or not.Design/methodology/approachThe design is by using Lawittes's and Schoeneberg's theorems.FindingsFinding all Weierstrass points on X0(N) fixed by some Atkin–Lehner involutions. Besides, the authors have listed them in a table.Originality/valueThe Weierstrass points have played an important role in algebra. For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. Finally, the set of Weierstrass points is useful in studying arithmetic and geometric properties of X0(N).

PurposeThis paper aims to prove some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results of this paper generalize and extend several known results to modular G-metric spaces, including the results of Mutluet al.[1]. Furthermore, the authors produce an example to demonstrate the applicability of the results.Design/methodology/approachThe results of this paper are theoretical and analytical in nature.FindingsThe authors established some fixed-point theorems for a general class of mappings in modular G-metric spaces. The results generalize and extend several known results to modular G-metric spaces, including the results of Mutluet al. [1]. An example was constructed to demonstrate the applicability of the results.Research limitations/implicationsAnalytical and theoretical results.Practical implicationsThe results of this paper can be applied in science and engineering.Social implicationsThe results of this paper is applicable in certain social sciences.Originality/valueThe results of this paper are new and will open up new areas of research in mathematical sciences.

PurposeIn this paper, we give some properties of the α-connections on statistical manifolds and we study the α-conformal equivalence where we develop an expression of curvature R¯ for ∇¯ in relation to those for ∇ and ∇^.Design/methodology/approachIn the first section of this paper, we prove some results about the α-connections of a statistical manifold where we give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds treated in [1, 3], and we construct some examples.FindingsWe give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.Originality/valueWe give some properties of the difference tensor K and we determine a relation between the curvature tensors; this relation is a generalization of the results obtained in [1]. In the second section, we introduce the notion of α-conformal equivalence of statistical manifolds, we give the relations between curvature tensors and we construct some examples.

PurposeIn this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.Design/methodology/approachThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.FindingsShowed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.Originality/valueThis new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

PurposeIn this article, the authors discuss the existence and multiplicity of solutions for an anisotropic discrete boundary value problem inT-dimensional Hilbert space. The approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.Design/methodology/approachThe approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.FindingsThe authors study the existence of results for a discrete problem, with two boundary conditions type. Accurately, the authors have proved the existence of at least three solutions.Originality/valueAn other feature is that problem is with non-local term, which makes some difficulties in the proof of our results.