# New type of multivalued F-contraction involving fixed points on closed ball

Volume 17, Issue 2, pp 246-254 Publication Date: June 15, 2017

### 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 Nazam - Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan.

### Abstract

This paper is a continuation of the investigations of F-contraction. The aim of this article is to extend the concept of F-contraction on closed ball. We introduce the notion of Ćirić type multivalued F-contraction on closed ball and establish new fixed point theorems for Ćirić type multivalued F-contraction 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 well-known results in the existing comparable literature.

### Keywords

• Metric space
• fixed point
• F-contraction
• closed ball.

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