The motivation of this paper is to introduce and study a new class of univalent functions equipped with conic type regions. We also investigate a number of useful properties of this class and coefficient estimates for functions. Several consequences of the results are also pointed out.

We give altenative proofs of results of G. Khimshiashvili and collaborators on polygonal linkages which are critical points for the area functional under various edge lengths constraints.

The main objective of this paper is to establish several new lower and upper bounds for the functions $\sinh x/x$ and $\cosh x$. Following the simple approach, our results give refinements and generalizations of some known inequalities involving these functions.

We show that assuming the consistency of certain large cardinals (namely a supercompact cardinal with a measurable cardinal above it of the appropriate Mitchell order) together with the Ultrapower Axiom UA introduced by Goldberg in [3], it is possible to force and construct choiceless universes of ZF in which the first two uncountable cardinals $\aleph_1$ and $\aleph_2$ are both measurable and carry certain fixed numbers of normal measures. Specifically, in the models constructed, $\aleph_1$ will carry exactly one normal measure, namely $\mu_\omega = \{x \subseteq \aleph_1 \mid x$ contains a club set$\}$, and $\aleph_2$ will carry exactly $\tau$ normal measures, where $\tau = \aleph_n$ for $n=0,1,2$ or $\tau = n$ for $n \ge 1$ an integer (so in particular, $\tau \le \aleph_2$ is any nonzero finite or infinite cardinal). This complements the results of [1] in which $\tau \ge \aleph_3$ and contrasts with the well-known facts that assuming AD + DC, $\aleph_1$ is measurable and carries exactly one normal measure, and $\aleph_2$ is measurable and carries exactly two normal measures.

In this article, the truncated exponential polynomials are taken as base with the Gould-Hopper polynomials to introduce a hybrid family of truncated exponential-Gould-Hopper polynomials. These polynomials are framed within the context of monomiality principle and their properties are established. Certain properties including operational representations, expansion formula, integral representation and summation formula are also derived for this family. Further, the graphs of these polynomials are drawn for different values of indices using MATLAB.

In this paper, we prove the existence and uniqueness of solutions for a class of impulsive fractional initial/boundary value problems of the Riesz-Caputo differential equation with anti-peroidic boundary condition. In the final section, we give some numerical examples to verify the theoretical results.

In this paper, some infinite product representations of certain transcendental functions (whose all possible zeros and $n$-th order differential coefficient at the point $x=0$, can be calculated easily) are obtained by using the theory of polynomial equations. This approach is novel as it is different from the approaches used by other authors.

In this paper, we have studied a Pál type (1; 0)-interpolation when first derivatives and function values are prescribed on the zeros of Laguerre Polynomials $L_{n}^{(\alpha)}(x), \alpha > -1$ and its derivative $(L_{n}^{(\alpha)})^{\prime}(x)$ respectively. Existence, uniqueness, explicit representation and a quantitative estimate of the interpolatory polynomial $R_{n, \alpha}(x)$ has been obtained.

In the present article, the author investigates some properties of fractional analytic function $g_{m}(z)^{\alpha}$, belonging to two new subclasses of m-fold symmetric starlike and convex functions in the open unit disk. In addition, properties of certain new subclass $T^{\alpha}_{m, n}(\beta)$, of m-fold symmetric bi-Bazilevic functions associated with modified sigmoid functions are considered while several other corollaries follow as simple consequences.

"How we can speak about the features of involute curve on space $TR^{3}$ by looking at the characteristics of the first curve $\alpha $?" In this paper, we investigate the answer of this question using by lifts. In this direction firstly, we define the involute curve of any curve with respect to the vertical, complete and horizontal lifts on space $R^{3}$ to its tangent space $TR^{3}=R^{6}.$ Secondly, we examine the Frenet-Serret aparatus $\left\{ T^{\ast }(s),N^{\ast }(s),B^{\ast }(s),\kappa ^{\ast },\tau ^{\ast }\right\} $ and the unit Darboux vector $\tilde{D}^{\ast }$ of the involute curve $\alpha ^{\ast }$ according to the vertical, complete and horizontal lifts on $TR^{3}$ depending on the lifting of Frenet-Serret aparatus $\left\{ T(s),N(s),B(s),\kappa ,\tau \right\} $ of the first curve $\alpha $ on space $R^{3}.$ In addition, we include all special cases the curvature $\kappa ^{\ast }(s)$ and torsion $\tau ^{\ast }(s)$ of the Frenet-Serret aparatus of the involute curve $\alpha ^{\ast }$ with respect to lifts on space $R^{3}$ to its tangent space $TR^{3}.$ As a result of this transformation on space $R^{3}$ to its tangent space $TR^{3}$, we could have some information about the features of involute curve of any curve on space $TR^{3}$ by looking at the characteristics of the first curve $\alpha$. Moreover, we get the transformation of the involute curves using by lifts on $R^{3}$ to tangent space $TR^{3}$. Finally, some examples are given for each curve transformation to validated our theorical claims.

The concept of nano topological spaces induced by different neighborhoods was originally proposed by Thivagar and Priyalatha. The endeavor of the current work is to propose a certain extension of the previous concept called $I$-nano topological spaces induced by different neighborhood. This concept based on ideals. Some important characteristics and significant properties of these spaces are presented. We provide a comparative study of the present spaces and the previous one. It turn out that every nano topological space induced by different neighborhoods is an $I$-nano topological space induced by different neighborhoods. Afterwards, to emphasize these results some counter examples are considered. An application from the real life problems is presented. Eventually, the notions of $j$-ideal generalized nano closed sets and its properties are studied.

We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs $(x,x')$ of points in $\mathbb R^n$ which satisfy $d(x,x')\ge \varepsilon$. We interpret this as two or three (depending on the parity of $n$) geodesic motion-planning rules for this configuration space. In the associated unordered configuration space, we need not prescribe that the points stay apart by $\varepsilon$. For this space, with a Euclidean-related metric, we show that geodesic motion-planning rules correspond to ordinary motion-planning rules on $RP^{n-1}$.

In this paper, first, a numerical method is presented for solving generalized linear and nonlinear second-order two point initial and boundary value problems. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions. The obtained operational matrix is used to reduce the linear or nonlinear equations with their initial or boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. Finally, the efficiency of the proposed method is indicated by some numerical examples.

In this paper, absolute matrix summability of an infinite series has been studied. A known theorem dealing with $|\bar{N},p_n|_{k}$ summability factors of an infinite series has been generalized. This new theorem also includes some results.

The paper deals with the notion of conformal semi-slant submersions from Lorentzian para Kenmotsu manifolds onto Riemannian manifolds. In this paper, we study the integrability of the distributions and the geometry of leaves manifolds. Further, we obtain the necessary and sufficient conditions for such submersions to be totally geodesic where characteristic vector field $\xi $ is vertical.

A basic goal of this paper is to study the tube surface with a null Cartan curve with respect to the Bishop frame in Minkowski 3-space $E_{1}^{3}$ and to compute some geometric features for this kind of the tube surface such as, the first and the second fundamental forms, the mean and the Gaussian curvatures. Furthermore, using the mean curvature $H$ and the Gaussian curvature $K$, we investigate $\Omega(K,H)-$ surface condition of the tube surface with the null Cartan curve due to the Bishop frame in Minkowski 3-space $E_{1}^{3}$.

In this paper we study and develop the retracting property in homotopy theory for finite topological semigroups by introducing the notions of $DS-$retract sets and $US-$retract sets. We show that these sets are stronger forms of strong $S-$deformation retract sets. Furthermore, we study the uniqueness of retraction maps and some topological properties for these retract sets.