The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian $α$-Sasakian manifold. We study some curvature properties of Lorentzian $α$-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, $\varphi$-symmetric, $\varphi$-projectively at Lorentzian $α$-Sasakian manifolds with respect to quartersymmetric metric connection. We also discuss Lorentzian $α$-Sasakian manifold admitting quarter-symmetric metric connection satisfying $\tilde{P}.\tilde{S} = 0$, where $\tilde{P}$ denote the projective curvature tensor with respect to quarter-symmetric metric connection.

In their pioneering work dated 2010 on the subject of bi-univalent functions, Srivastava et al. actually revived the study of the coefficient problems involving bi-univalent functions in recent years. Inspired by the pioneering work of Srivastava et al., there has been triggering interest to study the coefficient problems for many different subclasses of bi-univalent functions. Motivated largely by a number of sequels to the investigation by Srivastava et al., in this paper, we consider certain classes of bi-univalent functions to obtain the estimates of their second and third Taylor-Maclaurin coefficients. Further, certain special cases are also indicated. Some interesting remarks about the results presented here are also discussed.

In this article a new result $|A, p_{m}, q_{n};δ|_{k}$ on summability of doubly infinite lower triangular matrix has been establised which generalizes a theorem of E. Savas and B.E. Rhoades and subsequently a theorem of Paikray et al. on summability factor of double infinite weighted mean matrix.

In this paper, a shrinking projection algorithm based on the extragradient iteration method for finding a common element of the set of common fixed points of a finite family of asymptotically nonexpansive mappings and a generalized nonexpansive set-valued mapping and the set of solutions of equilibrium problem for pseudomonotone and Lipschitz-type continuous bifunctions is introduced and investigated in Hilbert spaces. Moreover, the strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field.

In this note, a characterization for boundary representations of a $C^*$-algebra for an operator system in terms of quasi hyperrigidity and separating property of the operator system is established.

We introduce the notion of an essentially generalized $λ$-slant Toeplitz operator on the Hilbert space $L^2$ for a general complex number $λ$, via the operator equation $λM_{z}X - XM_{z^{k}} = K$, $K$ being a compact operator on $L^2$ and $k(≥ 2)$ being an integer. We attempt to investigate some of the properties of this operator and also study its counterpart on $H^2$.

In the present paper, the notion of generalized $(s, m, φ)$-preinvex function is applied to establish some new Hermite-Hadamard type inequalities via $k$-fractional Riemann-Liouville integrals. At the end, some applications to special means are given. These results not only extend the results appeared in the literature, but also provide new estimates on these types.

In this study, we achieve the general solution and investigate Ulam-Hyers stabilities involving a general control function, sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms of the duodecic functional equation in quasi-$β$-normed spaces via fixed point method. We also illustrate a counter-example for non-stability of the duodecic functional equation in singular case.

The purpose of this work is to develop two new iterative methods for solving nonlinear equations which does not require any derivative evaluations. These composed formulae have seventh and eighth order convergence and desire only four function evaluations per iteration which support the Kung-Traub conjecture on optimal order for without memory schemes. Finally, numerical comparison is provided to show its effectiveness and performances over other similar iterative algorithms in high precision computation.

In this paper, we study congruence properties of overcubic partition pairs. Let $\bar{b}(n)$ denote the number of overcubic partition pairs of $n$. We will establish some new Ramanujan type congruences and several infinite families of congruences modulo powers of $2$ satisfied by $\bar{b}(n)$.

The aim of this paper is to obtain some new refinements of Hermite-Hadamard type inequalities via conformable fractional integrals. The class of functions used for deriving the inequalities have the preinvexity property. We also discuss some special cases.

In this paper among the other things, we give some sufficient and necessary conditions for an element of $L^{2}(K)$ to be a Parseval admissible vector, where $K$ is a locally compact hypergroup.

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

One of the famous mathematical inequality is Minkowski's inequality. It is an important inequality from both mathematical and application points of view. In this paper, a Minkowski type inequality for fuzzy and pseudo-integrals is studied. The established results are based on the classical Minkowski's inequality for integrals.

Generalizing distributions is important for applied statisticians and recent literature has suggested several ways of extending well-known distributions. We propose a new class of distributions called the Marshall-Olkin Burr X family, which yields exible shapes for its density such as symmetrical, left-skewed, right-skewed and reversed-J shaped, and can have increasing, decreasing,constant, bathtub and upside-down bathtub hazard rates shaped. Some of its structural properties including quantile and generating functions, ordinary and incomplete moments, and mean deviations are obtained. One special model of this family, the Marshall-Olkin-Burr-Lomax distribution, is investigated in details. We also derive the density of the order statistics. The model parameters are estimated by the maximum likelihood method. For illustrative purposes, three applications to real life data are presented.