In this paper, we investigate the distribution of zeros as well as the uniqueness problems of certain type of differential polynomials sharing a small function with finite weight. The result obtained improves and generalizes the recent results.

In this paper, we introduce and obtain the general solution of a new generalized mixed quadratic and quartic functional equation and investigate its stability in non-Archimedean $\mathcal{L}$-fuzzy normed spaces.

In the present paper we introduce some sequence spaces combining lacunary sequence, invariant means over $n$-normed spaces defined by Musielak-Orlicz function $\mathcal{M} = (M_{k})$. We study some topological properties and also prove some inclusion results between these spaces.

In this paper, defining new interesting classes, $\lambda$-pseudo bi-starlike functions with respect to symmetrical points and $\lambda$-pseudo bi-convex functions with respect to symmetrical points in the open unit disk $\mathbb U$, we obtain upper bounds for the initial coefficients of functions belonging to these new classes.

In this paper, we introduce a new extended generalized Burr III family of distributions in the so-called T-BurrIII{Y} family by using the quantile functions of a few popular distributions. We derive the general mathematical properties of this extended family including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Three new Burr III sub-families are then investigated, and four new extended Burr III models are discussed. The density of Burr III extended distributions can be symmetric, left-skewed, right-skewed or reversed-J shaped, and the hazard rate shapes can be increasing, decreasing, bathtub and upside-down bathtub. The potentiality of the newly generated distributions is demonstrated through applications to censored and complete data sets.

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-$(r; m, h)$-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on $m$-invex set is derived. By using the notion of generalized relative semi-$(r; m, h)$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

In this paper we introduce and study the Stancu type generalization of the integral type operators defined in (1.1). First, we obtain the moments of the operators and then prove the Voronovskaja type asymptotic theorem and basic convergence theorem. Next, the rate of convergence and weighted approximation for the above operators are discussed. Then, weighted $L_p$-approximation and pointwise estimates are studied. Further, we study the $A$-statistical convergence of these operators. Lastly, we give better estimations of the above operators using King type approach.

We present an existence theorem for at least one continuous solution for a coupled system of nonlinear functional (delay) integral equations of Urysohn-Stieltjes type.

The article aims to explore some new classes of differential and integral equations for some hybrid families of Legendre polynomials. Beginning with the recurrence relations and shift operators, the authors derived the differential, integro-differential and partial differential equations for the hybrid Legendre-Appell polynomials. Certain examples are framed for the hybrid Legendre-Bernoulli, Legendre-Euler and Legendre-Genocchi polynomials to show the applications of main results. Further, the homogeneous Volterra integral equations for the hybrid Legendre-Appell and other hybrid families of special polynomials are derived. The inclusion of integral equations is a bonus to this article.

In this paper we define a subclass of bi-univalent functions. Further, we find the estimates on the bounds $|a_{2}|$ and $|a_{3}|$, the Fekete-Szegö inequalities and the second Hankel determinant inequality for defined class of bi-univalent functions.

Our aim is to present some new properties of functions in $p$-calculus. The effects of a convex or monotone function on the $p$-derivative and vice versa and also the behavior of $p$-derivative in a neighborhood of a local extreme point are expressed. Moreover, mean value theorems for $p$-derivatives and $p$-integrals are proved.

In this paper we introduce anew form of soft supra compact spaces namely, soft supra compact spaces, soft supra closed spaces, soft supra lindelof spaces and soft supra generalized compactness. Furthermore, we study its several properties and characterizations in detail. Also, the invariance of these kinds of soft supra compact spaces under some types of soft mapping and their hereditary properties are also investigated.