Multi-valued versions of Nadler, Banach, Branciari and Reich fixed point theorems in double controlled metric type spaces with applications

Sahibzada Waseem Ahmad; Muhammad Sarwar; Thabet Abdeljawad; Gul Rahmat; Sahibzada Waseem Ahmad; Muhammad Sarwar; Thabet Abdeljawad; Gul Rahmat

doi:10.3934/math.2021029

AIMS Mathematics

2021, Volume 6, Issue 1: 477-499. doi: 10.3934/math.2021029

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Research article

Multi-valued versions of Nadler, Banach, Branciari and Reich fixed point theorems in double controlled metric type spaces with applications

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan
2.
Department of Mathematics and General Sciences, Price Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
5.
Department of Mathematics, Islamia College Peshawar, Peshawar, KPK, Pakistan

Received: 12 August 2020 Accepted: 06 October 2020 Published: 19 October 2020
MSC : Primary 47H10; Secondary 54H25

In the current work, the multi-valued version of well-known theorems of Nadler, Banach, Branciari and Reich are generalized to the scope of double controlled metric space. A double controlled metric space is a metric type space in which the right hand side of the triangle inequality is controlled by two functions. Furthermore, applications to existence of solution to Volterra integral inclusions and singular Fredholm integral inclusions of are obtained.
Citation: Sahibzada Waseem Ahmad, Muhammad Sarwar, Thabet Abdeljawad, Gul Rahmat. Multi-valued versions of Nadler, Banach, Branciari and Reich fixed point theorems in double controlled metric type spaces with applications[J]. AIMS Mathematics, 2021, 6(1): 477-499. doi: 10.3934/math.2021029

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Abstract

In the current work, the multi-valued version of well-known theorems of Nadler, Banach, Branciari and Reich are generalized to the scope of double controlled metric space. A double controlled metric space is a metric type space in which the right hand side of the triangle inequality is controlled by two functions. Furthermore, applications to existence of solution to Volterra integral inclusions and singular Fredholm integral inclusions of are obtained.

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