In this study, we introduce a new space $\left\vert A_{f}^{\theta}\right\vert_{k}$ by using factorable matrix and investigate its certain topological and algebraic structures where $\theta$ is a positive sequence. Also, we characterize some matrix operators on this space and determine their norms and the Hausdorff measure of noncompactness. In the particular case, we get some well known results.

This study deals with the validation of classical stabilities of various multiplicative inverse functional equations pertinent to Ulam stability theory of functional equations in the setting of non-Archimedean fields. Suitable counter-examples are demonstrated to disprove the invalidity of stability results of these equations for singular cases.

Absolute Cesàro-Riesz summability method has been introduced and later on used to established a theorem containing least set of sufficient conditions for absolute $\varphi$-Cesàro-Riesz summable factor of an infinite series. The result has also been validated with the published literature on $ \varphi-|\bar{N}, p_n|_k$ summable factor by reducing certain conditions in the presented result.

In this paper, three index three variable Hermite matrix based Sheffer polynomials (3I3VHMSP) are introduced by algebraic decomposition of exponential operators. The operational methods combined with the monomiality principle can be used to introduce 3I3VHMSP and also to establish rules of operational nature, framing the special polynomials within the context of particular solutions of generalized forms of partial differential equations of evolution type. The Appell and Sheffer sequences along with the operational formalism offer a powerful tool for investigation of the properties of a wide class of polynomials. Further, operational representation providing connections between 3I3VHMSP families and the known special polynomials are established, which are used to derive new identities and the results for the members of these new families. The approach presented is general.

In this paper, we consider a reaction diffusion equation with multiple nonlinearities. We prove a blow up and exponential growth of solution with negative initial energy. Our new results generalizes and improves earlier results.

In this paper, we determine and study the behavior of all admissible solutions of the difference equation $$x_{n+1}=\frac{x_{n}x_{n-2}}{ax_{n-2}+ bx_{n-3}},\quad n=0,1,\ldots,$$ where $a,b$ are positive real numbers and the initial conditions $ x_{-3},x_{-2},x_{-1},x_0$ are real numbers. We show when $a=b=1$ that, every admissible solution converges to $0$.

In this paper, we study the uniqueness of a differential polynomial and monomial sharing a small function with finite weight and obtain two theorems which extend and improves the results of Harina P. Waghamore and Husna V [6].

In this paper, we are revisiting Meir-Keeler type fixed operators in the setting of Branciari distance space. The presented results improve and generalize several existing results in the literature. We consider an example to illustrate our result.

New sets of orthogonal functions, derived from the first and second kind Chebyshev polynomials, considering half-integer indexes, have been recently introduced. In this article several properties of these new sets are considered and the links with the classical Chebyshev polynomials are underlined.

The Hilali conjecture claims that a simply connected rationally elliptic space $X$ satisfies the inequality $\dim (\pi_*(X)\otimes \mathbb{Q} ) \leqq \dim H_*(X;\mathbb{Q} )$. In this paper we show that for any such space $X$ there exists a positive integer $n_0$ such that for any $n \geqq n_0$ the strict inequality $\dim (\pi_*(X^n)\otimes \mathbb{Q} ) \lt \dim H_*(X^n; \mathbb{Q} )$ holds, where $X^{n}$ is the product of $n$ copies of $X$.

In this paper, fractional residual power series method (FRPSM) is effectively applied for finding the approximate analytical solutions of general nonlinear time-fractional wave-like equations with variable coefficients. This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without need of linearization, discretization, perturbation or unrealistic assumptions. Numerical results are given and then they are compared with the exact solutions both numerically and graphically. By numerical examples, it is shown that the FRPSM is very simple, efficient and convenient for solving different forms of nonlinear fractional partial differential equations.

In this paper, we investigate the blow-up of solutions of a time-fractional nonlocal reaction-diffusion equation with variable exponents under the Dirichlet boundary condition. We prove the existence of a solution using the Banach fixed point theorem. Finally, we estimate the blow-up of solutions of the considered model using the Kaplan method.

In this paper first, we prove some new refinement of Hermite-Hadamard type inequalities for the convex function $f$. Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to $f$-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations and improvements of the earlier results.

In the present paper we shall investigate the pointwise approximation properties of the q analogue of the Bernstein-Durrmeyer operators and estimate the rate of pointwise convergence of these operators to the functions $f$ whose q-derivatives are bounded variation on the interval $[0,1]$. We give an estimate for the rate of convergence of the operator $\left( L_{n,q}f \right)$ at those points $x$ at which the one sided q-derivatives $ D_{q}^{+}f(x),D_{q}^{-} f(x)$ exist. We shall also prove that the operators $L_{n,q}f$ converges to the limit $f(x).$ To the best of my knowledge, the present study will be the first study on the approximation of q- operators in the space of $D_{q}BV$.

In this study, the author used the joint Fourier- Laplace transform to solve non-homogeneous time fractional first order partial differential equation with non-constant coefficients. Constructive examples are also provided throughout the paper. It is a remarkable feature of the first order fractional differential equations that a procedure can be developed for solving this equation, regardless of its complexity.

In this study, we investigate the tangent, principal normal and trinormal spherical images of a W-partially null curve in pseudohyperbolic space $\mathbb{H}_{0}^{3}$ of Minkowski space time $\mathbb{E}_{1}^{4}$. The tangent, principal normal spherical images of a W-partially null curve occur as spacelike curves lying in pseudosphere $\mathbb{S}_{0}^{3}$, then the Frenet-Serret invariants of the mentioned image curves are obtained in terms of the invariants of W-partially null curve. The trinormal spherical images of a W-partially null curve occur as spacelike curves lying in pseudohyperbolic space $\mathbb{H}_{0}^{3}$, then the Frenet-Serret invariants of the mentioned image curves are obtained in terms of the invariants of W-partially null curve. Finally, we give some characterizations of the spherical images being helices.

Using the results of S. S. Bhoosnurmath, we mainly study the uniqueness of entire and meromorphic functions that share small functions with their homogeneous and linear differential polynomials. In this paper, we obtain significant improvements and generalizations of the results of H. X. Yi.