New type of multivalued Fcontraction involving fixed points on closed ball
Authors
Aftab Hussain
 Department of Mathematical Sciences, Lahore Leads University, Lahore  54000, Pakistan.
Hafiz Farooq Ahmad
 College of Computer Sciences and Information Technology (CCSIT) King Faisal University, Alahssa 31982, Kingdom of Saudi Arabia.
Muhammad Arshad
 Department of Mathematics, International Islamic University, H10, Islamabad  44000, Pakistan.
Muhammad Nazam
 Department of Mathematics, International Islamic University, H10, Islamabad  44000, Pakistan.
Abstract
This paper is a continuation of the investigations of Fcontraction. The aim of this article is to extend the concept of Fcontraction on closed ball. We introduce the notion of Ćirić type multivalued Fcontraction on closed ball and establish new
fixed point theorems for Ćirić type multivalued Fcontraction on closed ball in a complete metric space. Our results are very
useful for the contraction of the mapping only on closed ball instead on the whole space. Some comparative examples are
constructed whose illustrate the superiority of our results. Our results provide extension as well as substantial generalizations
and improvements of several wellknown results in the existing comparable literature.
Keywords
 Metric space
 fixed point
 Fcontraction
 closed ball.
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