Some applications of fixed point results for monotone multivalued and integral type contractive mappings

Abstract

Abstract The motivation of the present paper is to introduce and establish some new fixed point results for monotone multivalued functions in partially ordered complete $D^{*}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -metric spaces, where the partial ordered set $(X,\leq )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mo>≤</mml:mo> <mml:mo>)</mml:mo> </mml:math> is obtained via a pair of functions $( \Upsilon,\Omega )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:mi>ϒ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Ω</mml:mi> <mml:mo>)</mml:mo> </mml:math> . Moreover, several existence and uniqueness coupled fixed point theorems of mappings satisfying contractive conditions have been investigated and verified in the setting of partially ordered complete $D^{*}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -metric spaces by using the concept of integral type contractions with respect to partially ordered $D^{*}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> -metric space. Furthermore, we present appropriate examples as an application for our main results. Our results generalize the work of Ghasab, Majani, and Rad on the study of integral type contraction and coupled fixed point theorems in the ordered G -metric spaces.