Equivalence results for implicit Jungck–Kirk type iterations

We show that the implicit Jungck–Kirk-multistep, implicit Jungck–Kirk–Noor, implicit Jungck–Kirk–Ishikawa, and implicit Jungck–Kirk–Mann iteration schemes are equivalently used to approximate the common fixed points of a pair of weakly compatible generalized contractive-like operators defined on normed linear spaces. Our results contribute to the existing results on the equivalence of fixed point iteration schemes by extending them to pairs of maps. An example to show the applicability of the main results is included

SOME CLASSES OF CONVEX FUNCTIONS ON TIME SCALES

We have introduced diamond $\phi_{h-s, \mathbb{T}}$ derivative and diamond $\phi_{h-s,\mathbb{T}}$ integral on an arbitrary time scale. Moreover, various interconnections with the notion of classes of convex functions about these new concepts are also discussed

STRONG CONVERGENCE THEOREM FOR UNIFORMLY L-LIPSCHITZIAN MAPPING OF GREGUS TYPE IN BANACH SPACES

In this paper, we introduced a new mapping called Uniformly L-Lipschitzian mapping of Gregus type, and used the Mann iterative scheme to approximate the fixed point. A Strong convergence result for the sequence generated by the scheme is shown in real Banach space. Our result generalized and unifybmany recent results in this area  of research. In addition, using Java(jdk1.8.0_101), we give a numericalbexample to support our claim

On Some New Extensions and Generalizations of Eneström-Kakeya Theorem

In this paper we obtain some new extensions and generalizations of the well-known classical theorem of Eneström and Kakeya.Keywords and Phrases: Complex number, Polynomial, Zeros, Eneström-Kakeya theorem, Bounds, Modulii, Dis

On Equivalence of the Ap-Sequential Henstock and Ap-Sequential Topological Henstock Integrals: Equivalence of the Ap-Sequential Henstock and Ap-Sequential Topological Henstock Integrals

Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is a function defined in a complete space $\Omega$ and $\tau$ is a vector in $\mathbb{R}$ taking values in $X$. Suppose $f$ is ap-Sequential Henstock integrable with respect to $\tau$, is $f$ ap-Sequential Topological Henstock integrable with respect to $\tau$? It is the purpose of this paper to proffer affirmative answer to this question