Abstract
We present fixed points results of multivalued Prešić type k-step iterative mappings satisfying generalized weakly contraction conditions in metric spaces. An example is presented to support the main result proved herein. The stability of fixed point sets of multivalued Prešić type weakly contractive mappings are also established. Global attractivity result for the class of matrix difference equations is derived as application of the result presented herein. These results generalize and extend various comparable results in the existing literature.
Highlights
Introduction and PreliminariesA Banach contraction principle [1] is the simplest and useful tool having a variety of scientific applications such as proving the existence of the solution of linear, nonlinear, differential, integral, and difference equations
Kannan [2] established fixed point theorem on certain type of contraction mappings that are independent of the Banach contraction principle
The aim of this paper is to introduce the concept of Prešić type weakly contractive multivalued mappings and to study the fixed point result for such mappings in metric spaces
Summary
Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan Department of Mathematics, Government College University, Lahore-54000, Pakistan Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield, Pretoria 002, South Africa
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