


Paper's Title:
A new approach to the study of fixed point for simulation functions with application in Gmetric spaces
Author(s):
Komi Afassinou and Ojen Kumar Narain
Department of Mathematical Sciences,
University of Zululand,
KwaDlangezwa,
South Africa.
Email: komia@aims.ac.za
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
Abstract:
The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)Zcontraction mapping, Suzuki generalized (α,β)Zcontraction mapping, (α,β)admissible mapping and triangular (α,β)admissible mapping in the frame work of Gmetric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete Gmetric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.
Paper's Title:
Existence of Solution of Differential and RiemannLiouville Equation Via Fixed Point Approach in Complex Valued bMetric Spaces
Author(s):
K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain
Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
Email: komia@aims.ac.za
DSTNRF Centre of Excellence in
Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: dele@aims.ac.za
DSTNRF Centre of Excellence in
Mathematical and Statistical Sciences (CoEMaSS),
Johannesburg,
South Africa.
Email: hammedabass548@gmail.com
School of Mathematics, Statistics and
Computer Science,
University of KwaZuluNatal, Durban,
South Africa.
Email: naraino@ukzn.ac.za
Abstract:
In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of Cclass function in the framework of complex valued bmetric spaces. As an application, we establish the existence and uniqueness of a solution for RiemannLiouville integral and ordinary differential equation in the framework of a complete complex valued bmetric spaces. The obtained results generalize and improve some fixed point results in the literature.
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