Let $X$ be a weakly Cauchy normed space in which the parallelogram law holds, $C$ be a bounded closed convex subset of $X$ with one contracting point and $T$ be an $\{a,b,c\}$-generalized-nonexpansive mapping from $C$ into $C$. We prove that the infimum of the set $\{\| x-T(x) \|\}$ on $C$ is zero, study some facts concerning the $\{a,b,c\}$-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to $C$ is singleton. Depending on the fact that the $\{a,b,0\}$-generalized-nonexpansive mapping from $C$ into $C$ has fixed points, accordingly, another version of the Browder's strong convergence theorem for mappings is given.

In this paper, we introduce two hybrid iterative algorithms of Jungck-Kirk-Mann (J-K-M) and Jungck-Kirk (J-K) types to obtain some stability results for non-self mappings by employing a certain general contractive condition. Our results generalize and extend most of the existing ones in the literature.

In this paper, we introduce new sufficient conditions for certain integral operators to be starlike and  $p$-valently starlike in the open unit disk.

The order of magnitude of multiple Fourier coefficients of complex valued functions of generalized bounded variations like $(\Lambda^1,\cdots, \Lambda^N)BV^{(p)}$ and $r-BV$, over $[0, 2\pi]^{N},$ are estimated.

Let $P(z)$ be a polynomial of degree $n$ having no zeros in $|z|< 1$, then for every real or complex number $\beta$ with $|\beta|\leq 1$, and $|z|=1$, $R\geq 1$, it is proved by Dewan et al. [4] that$$\Big|P(Rz)+\beta\Big(\frac{R+1}{2}\Big)^n P(z)\Big|\leq\frac{1}{2}\Big\{\Big(\Big|R^n+\beta\Big(\frac{R+1}{2}\Big)^n\Big|+\Big|1+\beta\Big(\frac{R+1}{2}\Big)^n\Big|\Big)\max_{|z|=1}|P(z)|$$ $$-\Big(\Big|R^n+\beta\Big(\frac{R+1}{2}\Big)^n\Big|-\Big|1+\beta\Big(\frac{R+1}{2}\Big)^n\Big|\Big)\min_{|z|=1}|P(z)|\Big\}.$$ In this paper we generalize the above inequality for polynomials having no zeros in $|z| < k$, $k\leq 1$. Our results generalize certain well-known polynomial inequalities.

We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arzela-Ascoli theorem to show a fixed point theorem of Schauder.

In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO$(\mu)$ function on homogeneous Morrey-Herz spaces with non doubling measures.

Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbf R^n)$ with Gaussian kernel bound, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0 < \alpha < n$. In this paper, we will obtain some boundedness properties of commutators $\big[b,L^{-\alpha/2}\big]$ on weighted Morrey spaces $L^{p,\kappa}(w)$ when the symbol $b$ belongs to $BMO(\mathbf R^n)$ or the homogeneous Lipschitz space.

The aim of this work is to generalize Szász-Mirakian operator in the sense of Stancu-Durrmeyer operators. We obtain approximation properties of these operators. Here we study asymptotic as well as rate of convergence results in simultaneous approximation for these modified operators.