This paper develops a novel Bullen inequality for third-differentiable functions using Riemann integrals. Furthermore, new Bullen inequalities are proposed utilizing a summation parameter p ? 1 for and s-convex functions,convex functions and P-functions classes. Particular cases are studied when the third derivative functions are also bounded and Lipschitzian.

In this note, we define two distinct categories of fuzzy Z-proximal contractions and we use these two fuzzy Z-proximal contractive inequalities as a tool to obtain best proximity point for a non-self mapping which is defined between two distinct non-empty subsets of a strong fuzzy metric space. Further, prove some proximity theorems by using these categories of fuzzy Z-proximal in a complete strong fuzzy metric space. For the support of these innovative results we produce a few validation of examples. At last, we provide a solution of a non-linear second-order ordinary differential equation with the help of fuzzy Z-proximal contractive inequality provided that assumed space is strong fuzzy metric space.

We investigate the class of star-dagger operators for which A* and A? commute. Let A = U|A|be the polar decomposition, ?(s, t) = |A|sU|A|t be the generalized Aluthge transformation, and ?(*)(s, t) =|A*|sU|A*|t be the generalized *-Aluthge transformation of A, respectively. We have discovered new characterizationsfor star-dagger operators, specifically that A is a star-dagger operator if and only if U and Acommute. In this particular case, we have proven that ?(s, t) = PR(A*)A and ?(*)(s, t) = APR(A) when s, t > 0 and s + t = 1.

In this paper, we introduce the concept of pseudo-irreducible ideals in residuated lattices and obtain its relationship with important concepts such as prime ideals and maximal ideals in residuated lattices. We then use this concept to define and study complete comaximal decomposition in residuated lattices. Specifically, we characterize residuated lattices in which proper ideals can be expressed as the intersection of pairwise comaximal of finitely many pseudo-irreducible ideals.

Multiple object tracking (MOT) depends heavily on selection of true positive detected bounding boxes. However, this aspect of the problem is mostly overlooked or mitigated by employing two-stage association and utilizing low confidence detections in the second stage. Recently proposed BoostTrack attempts to avoid the drawbacks of multiple stage association approach and uses low-confidence detections by applying detection confidence boosting. In this paper, we identify the limitations of the confidence boost used in BoostTrack and propose a method to improve its performance. To construct a richer similarity measure and enable a better selection of true positive detections, we propose to use a combination of shape, Mahalanobis distance and novel soft BIoU similarity. We propose a soft detection confidence boost technique which calculates new confidence scores based on the similarity measure and the previous confidence scores, and we introduce varying similarity threshold to account for lower similarity measure between detections and tracklets which are not regularly updated. The proposed additions are mutually independent and can be used in any MOT algorithm. Combined with the BoostTrack+ baseline, our method achieves near state of the art results on the MOT17 dataset and new state of the art HOTA and IDF1 scores on the MOT20 dataset. The source code is available at: https://github.com/vukasin-stanojevic/BoostTrack.

This article explores the existence of an optimal solution for our proposed system of integro differential equations in Banach space by generalizing the best proximity point (pair) theorem and utilizing a new contraction operator. With the aid of an appropriate example, the applicability of our findings has also been demonstrated.

Recently, Gutman constructed six novel graph invariants in view of geometric arguments and defined them as Sombor-index-like graph invariants, denoted by S1O, S2O,???, S6O. Compared with some popular and commonly used indices, nearly all these six graph invariants have high accuracy in predicting physical and chemical properties. Therefore, in this article, we obtain a lower bound on four Sombor-index-like graph invariants (S1O, S2O, S5O and S6O) for all chemical (n, m, k)-graphs (chemical graphs of order n having m edges and k pendent vertices), and characterize those chemical (n, m, k)-graphs achieving the extremal value.

Applying the fixed point theorem, we offer the existence of solutions of an infinite system of mixed Volterra-Fredholm type of nonlinear integral equations in the sequence space c0. To further demonstrate the given existence result, we provided examples.

Let K be a compact subgroup of a locally compact group G. We investigate topologically invariant ?-means (with norm one) over the dual of the Lebesgue-Fourier algebra related to coset spaces G/K, where ? is a nonzero character of the Lebesgue-Fourier algebra on G/K. We prove that the set of all topologically invariant ?-means over dual of the Fourier algebra of G/K and the set of all topologically invariant ?-means over the dual of the Lebesgue-Fourier algebra of G/K have the same cardinality. Furthermore, we introduce and study the spaces weakly almost periodic functionals and uniformly continuous functionals over the Lebesgue-Fourier algebra of G/K.

Soft sets and statistical convergence are both mathematical tools with which some generalizations can be made. In this study, we defined the weighted statistical convergence of soft point sequences in soft topological spaces and examined it from some aspects. Furthermore, statistical convergence was attained using 1-density, a more versatile density function than asymptotic density. Regarding weighted soft statistical convergence concept, we also establish some relationships between soft topology and the classical topology induced by it within the framework of the statistical convergence concept and some clusters associated with statistical convergence were defined.