Affiliations: [a] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
| [b] Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria
| [c] Department of Mathematics, COMSATS University, Chak Shahzad, Islamabad, Pakistan
Correspondence:
[*]
Corresponding author. Shehu Shagari Mohammed, Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria. E-mail: ssmohammed@abu.edu.ng.
Abstract: As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.
Keywords: 46S40, 47H10, 54H25
Keywords: e-soft fixed point, e-continuous, F-contraction, soft set-valued map, αe-admissible, integral inclusion
