New Extensions of Kannan's and Reich's Fixed Point Theorems for Multivalued Maps Using Wardowski's Technique with Application to Integral Equations
Date
2020
Authors
Debnath, Pradip
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
The metric function generalizes the concept of distance between two points and hence
includes the symmetric property. The aim of this article is to introduce a new and proper extension
of Kannan’s fixed point theorem to the case of multivalued maps usingWardowski’s F-contraction.
We show that our result is applicable to a class of mappings where neither the multivalued version of
Kannan’s theorem nor that of Wardowski’s can be applied to determine the existence of fixed points.
Application of our result to the solution of integral equations has been provided. A multivalued
Reich type generalized version of the result is also established.
Description
Keywords
fixed point, multivalued map, F-contraction, complete metric space, integral equation
Citation
Debnath, P., & Srivastava, H. M. (2020). New Extensions of Kannan’s and Reich’s Fixed Point Theorems for Multivalued Maps Using Wardowski’s Technique with Application to Integral Equations. Symmetry, 12(7), 1-9. https://doi.org/10.3390/sym12071090.